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Silviu-iulian Niculescu - One of the best experts on this subject based on the ideXlab platform.
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Multiplicity-Induced-Dominancy extended to neutral delay equations: Towards a systematic PID tuning based on Rightmost root assignment
2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
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ACC - Multiplicity-Induced-Dominancy Extended to Neutral Delay Equations: Towards a Systematic PID Tuning Based on Rightmost Root Assignment
2020 American Control Conference (ACC), 2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
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Multiplicity-Induced-Dominancy in parametric second-order delay differential equations: Analysis and application in control design
ESAIM: Control Optimisation and Calculus of Variations, 2019Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Ali El Ati, Redamy Pérez-ramos, Karim Liviu TrabelsiAbstract:This work revisits recent results on maximal multiplicity induced-dominancy for Spectral Values in reduced-order time-delay Systems and extends it to the general class of second-order retarded differential equations. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the parameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.
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Towards a Decay Rate Assignment Based Design for Time-Delay Systems with Multiple Spectral Values
2018Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Karim TrabelsiAbstract:Recent results on maximal multiplicity induced-dominancy for Spectral Values in reduced-order Time-Delay Systems naturally apply in controllers design. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value, then, the dominancy is shown using the argument principle. Various reduced order examples illustrate the applicative perspectives of the approach.
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On the Dominancy of Multiple Spectral Values for Time-delay Systems with Applications
IFAC-PapersOnLine, 2018Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A further extension of a result on maximal multiplicity induced-dominancy for Spectral Values is analytically derived for generic retarded second-order systems with a single delay in the parameter space. Several examples illustrate the applicative perspectives of the result, towards a rightmost Spectral Value assignment approach.
Islam Boussaada - One of the best experts on this subject based on the ideXlab platform.
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Multiplicity-Induced-Dominancy extended to neutral delay equations: Towards a systematic PID tuning based on Rightmost root assignment
2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
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ACC - Multiplicity-Induced-Dominancy Extended to Neutral Delay Equations: Towards a Systematic PID Tuning Based on Rightmost Root Assignment
2020 American Control Conference (ACC), 2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
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Multiplicity-Induced-Dominancy in parametric second-order delay differential equations: Analysis and application in control design
ESAIM: Control Optimisation and Calculus of Variations, 2019Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Ali El Ati, Redamy Pérez-ramos, Karim Liviu TrabelsiAbstract:This work revisits recent results on maximal multiplicity induced-dominancy for Spectral Values in reduced-order time-delay Systems and extends it to the general class of second-order retarded differential equations. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the parameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.
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Towards a Decay Rate Assignment Based Design for Time-Delay Systems with Multiple Spectral Values
2018Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Karim TrabelsiAbstract:Recent results on maximal multiplicity induced-dominancy for Spectral Values in reduced-order Time-Delay Systems naturally apply in controllers design. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value, then, the dominancy is shown using the argument principle. Various reduced order examples illustrate the applicative perspectives of the approach.
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On the Dominancy of Multiple Spectral Values for Time-delay Systems with Applications
IFAC-PapersOnLine, 2018Co-Authors: Islam Boussaada, Silviu-iulian NiculescuAbstract:A further extension of a result on maximal multiplicity induced-dominancy for Spectral Values is analytically derived for generic retarded second-order systems with a single delay in the parameter space. Several examples illustrate the applicative perspectives of the result, towards a rightmost Spectral Value assignment approach.
A.j. Pritchard - One of the best experts on this subject based on the ideXlab platform.
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Gershgorin–Brualdi perturbations and Riccati equations
Linear Algebra and its Applications, 2007Co-Authors: Diederich Hinrichsen, A.j. PritchardAbstract:For uncertain linear systems with complex parameter perturbations of static output feedback type a quadratic Liapunov function of maximal robustness was constructed in [D. Hinrichsen, A.J. Pritchard, Stability radius for structured perturbations and the algebraic Riccati equation, Syst. Control Lett. 8 (1986) 105–113]. Such Liapunov functions can be used to ensure the stability of uncertain systems under arbitrary nonlinear and time-varying perturbations which are smaller than the stability radius. In this paper we establish analogous results for structured Gershgorin–Brualdi type perturbations of diagonal matrices where all the matrix entries at an arbitrarily prescribed set of positions are independently perturbed. We also derive explicit and computable formulae for the associated μ-Values, stability radii and Spectral Value sets.
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CDC - Stability radii and Spectral Value sets for generalized Gershgorin perturbations
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: M. Karow, Diederich Hinrichsen, A.j. PritchardAbstract:In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin type perturbations"). We derive explicit and computable formulae for the associated ?-Values. The results are then applied to characterize Spectral Value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case the classical eigenValue inclusion theorem of Brualdi is obtained as a corollary.
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Interconnected Systems with Uncertain Couplings: Explicit Formulae for mu -Values, Spectral Value Sets, and Stability Radii
SIAM Journal on Control and Optimization, 2006Co-Authors: Michael Karow, Diederich Hinrichsen, A.j. PritchardAbstract:In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin-type perturbations"). We derive explicit and computable formulae for the associated mu-Values. The results are then applied to characterize Spectral Value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case, the classical eigenValue inclusion theorems of Gershgorin, Brauer, and Brualdi are obtained as corollaries. Moreover it follows that the inclusion regions of Brauer and Brualdi are optimal for the corresponding perturbation structures.
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Spectral Value sets of closed linear operators
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2000Co-Authors: E. Gallestey, D. Hinrichsen, A.j. PritchardAbstract:We study how the spectrum of a closed linear operator on a complex Banach space changes under affine perturbations of the form A ↝ AΔ = A + DΔE. Here A, D and E are given linear operators, whereas Δ is an unknown bounded linear operator that parametrizes the possibly unbounded perturbation DΔE. The union of the spectra of the perturbed operators AΔ, with the norm of Δ smaller than a given δ > 0, is called the Spectral Value set of A at level δ. In this paper we extend a known characterization of these sets for the matrix case to infinite dimensions, and in so doing present a framework that allows for unbounded perturbations of closed linear operators on Banach spaces. The results will be illustrated by applying them to a delay system with uncertain parameters and to a partial differential equation with a perturbed boundary condition.
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Spectral Value sets of infinite-dimensional systems
Open Problems in Mathematical Systems and Control Theory, 1999Co-Authors: E. Gallestey, D. Hinrichsen, A.j. PritchardAbstract:We assume that X, X, U, Y are complex or real separable Banach spaces, A with dense domain D(A) ⊂ X is a closed linear operator on X, D(A) ⊂ X ⊂ X with continuous dense injections, B ∈ ℒ(U,X) and C ∈ ℒ (X,Y). Let K denote the field of scalars. Our subject is the variation of the spectrum, σ(A) under structured perturbations of the form $$ A \rightsquigarrow {A_\Delta } = A + B\Delta C,\,\,\Delta \in \mathcal{L}\left( {Y,U} \right) $$ (23.1) where D(A Δ) = D(A). The operators B, C are fixed and describe both the structure and unboundedness of the perturbations, whilst Δ ∈ ℒ (Y, U) is arbitrary. If U = X = X = Y, B = I x = C, i.e. A Δ = A + Δ, Δ ∈ ℒ (X) the perturbations are bounded and are said to be unstructured.
Hui-chin Tang - One of the best experts on this subject based on the ideXlab platform.
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Dimensionality of Spectral Test for a Linear Congruential Random Number Generator
Journal of Discrete Mathematical Sciences and Cryptography, 2014Co-Authors: Hui-chin Tang, Yi-fang Chen, Kuang-hang HsiehAbstract:AbstractThis paper considers the successive dimensions of the Spectral test for a linear congruential generator (LCG) based on three types of the upper bound on the center density. We conduct an exhaustive search for the maximum and difference normalized Spectral Value in dimensions 2, 3, …, 32 of an LCG. The experimental result indicates that the appropriate dimensions for implementing the Spectral test are 2, 3, …, 8 with the objective of maximizing the normalized Spectral Value.
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an exhaustive analysis of two term multiple recursive random number generators with double precision floating point restricted multipliers
Journal of Discrete Mathematical Sciences and Cryptography, 2011Co-Authors: T C Kao, Hui-chin TangAbstract:Abstract This paper performs an exhaustive search for the maximum Spectral Value in full period two-term k th-order multiple recursive generators (kMRGs) with the double precision floating point (DF) restricted multipliers for orders k = 2, 3, …, 7. For a two-term kMRG, computational experiment is conducted to compare and evaluate the numbers of the number of possible multipliers and the Spectral Values with those of the approximate factoring (AF) restricted multipliers. According to the experiments we perform, the results indicate differences exist among the numbers of possible multipliers for the AF and DF multiplier restrictions. We demonstrate that these differences can affect the performance of Spectral tests.
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A partial exhaustive search for good two-term third-order multiple recursive random number generators
Journal of Discrete Mathematical Sciences and Cryptography, 2011Co-Authors: Hui-chin Tang, K. H. Hsieh, C. J. WangAbstract:Abstract This paper considers the problem of searching for a vector of multipliers in a two-term third-order multiple recursive generator (3MRG) with the objective of maximizing the Spectral test performance. On computers with double precision floating point, the maximum Spectral Value can serve as an initial threshold one. The Spectral Value found by this paper is superior to the best Spectral Value previously published for the full period 3MRG.
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A backward heuristic algorithm for two-term multiple recursive random number generators
Journal of Discrete Mathematical Sciences and Cryptography, 2010Co-Authors: Hui-chin Tang, K. H. Hsieh, T. L. ChaoAbstract:Abstract This paper considers the problem of searching for the maximum Spectral Value in a full period two-term kth-order multiple recursive generator with the unrestricted multipliers. The maximum Spectral Value with the double precision floating-point restricted multipliers can serve as an initial threshold Spectral Value. Based on equivalence properties of full period and Spectral test, a backward heuristic algorithm with the threshold Spectral Value for efficiently calculating Spectral Value and checking full period is presented and is suitable for the parallel computations.
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Full period and Spectral test of linear congruential generator and second-order multiple recursive generator
Journal of Information and Optimization Sciences, 2009Co-Authors: Hui-chin Tang, Chi-chi ChenAbstract:We analyze the periodicity and Spectral Value of linear congruential generator (LCG) and second-order multiple recursive generator (2MRG). Either LCG or 2MRG has an associated generator that possesses the same periods and Spectral Values. Based on this equivalence property, computational effort required for the full period LCG and 2MRG with maximum Spectral Value criterion is reduced by half.
Jie Chen - One of the best experts on this subject based on the ideXlab platform.
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Multiplicity-Induced-Dominancy extended to neutral delay equations: Towards a systematic PID tuning based on Rightmost root assignment
2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
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ACC - Multiplicity-Induced-Dominancy Extended to Neutral Delay Equations: Towards a Systematic PID Tuning Based on Rightmost Root Assignment
2020 American Control Conference (ACC), 2020Co-Authors: Islam Boussaada, Silviu-iulian Niculescu, Catherine Bonnet, Jie ChenAbstract:Recently, the conditions on a multiple Spectral Value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real Spectral Value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost Spectral Value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate.
