The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Tong Zhou - One of the best experts on this subject based on the ideXlab platform.
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Spatially Interconnected Systems Positive on a Quadratically Constrained Frequency Domain
IFAC Proceedings Volumes, 2020Co-Authors: Tong ZhouAbstract:Abstract Generalized Positiveness is investigated in this paper for a spatially interconnected system (SIS). Results of Zhou [2009] are extended to a more general frequency domain and more complicated requirements on the frequency response of a SIS. Based on an alternative characterization of the desirable frequency domain, a linear matrix inequality (LMI) based sufficient condition is derived for the weighted Positiveness of a SIS over a frequency domain described by several matrix valued quadratic functions. Moreover, using the separability property of convex sets, situations have also been clarified under which this sufficient condition becomes also necessary.
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generalized Positiveness of spatially interconnected systems over quadratically constrained frequency domains
Systems & Control Letters, 2012Co-Authors: Tong ZhouAbstract:Abstract Generalized Positiveness is investigated in this paper for a spatially interconnected system (SIS). Results of [7] are corrected and extended to a more general frequency domain and to more complicated requirements on the frequency response of a SIS. Based on an equivalent characterization of the interested frequency domain, a linear matrix inequality (LMI) based sufficient condition is derived for the generalized Positiveness of a SIS over a frequency domain described by several matrix valued quadratic functions. Moreover, using the separability property of convex sets, situations have also been clarified under which this sufficient condition becomes also necessary.
Vikram Sharma - One of the best experts on this subject based on the ideXlab platform.
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improved bounds on absolute Positiveness of multivariate polynomials
Journal of Symbolic Computation, 2019Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:Abstract A multivariate polynomial F ( x 1 , x 2 , … , x n ) is said to be absolutely positive from a real number B if F and all its partial derivatives are non-negative for x 1 , x 2 , … , x n ≥ B . One of the well known bounds on absolute Positiveness in the literature is due to Hong. His bound is dependent on the largest number in a certain sequence of radicals defined using the absolute value of the coefficients of the polynomial. In the univariate setting, a bound due to Lagrange considers the first and the second largest numbers in the same radical sequence and is shown by Collins to be better than Hong's bound. In the 1930's, Westerfield had proposed a bound that considers every value in the same radical sequence and improves on Lagrange's bound. In this paper, we provide a hierarchy of bounds generalizing Westerfield's bound to the multivariate setting. One of the bounds in this hierarchy is a generalization of Lagrange's bound. All the bounds are strict quantitative improvements over Hong's bound. We also give an algorithm to compute the multivariate Lagrange bound. The running time of this algorithm matches the running time of the best known algorithm to compute Hong's bound. The algorithm uses the range tree data structure to implement orthogonal range querying. Relying on a result of Fredman (1984), we show that the efficiency of this algorithm cannot be improved by using any other data structure for orthogonal range querying.
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improved bounds on absolute Positiveness of multivariate polynomials
International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:A multivariate polynomial F(x1,x2,...,xn) is said to be absolutely positive from a real number B if F and all its partial derivatives are non-negative for x1,x2,...,xn ≥ B. One of the well known bounds on absolute Positiveness in the literature is due to Hong. His bound is dependent on the first maximum of a certain sequence of radicals defined using the absolute value of the coefficients of the polynomial. In the univariate setting, a bound due to Lagrange considers the first and the second maximum in the same radical sequence and is shown by Collins to be better than Hong's bound. In the 1930's, Westerfield had proposed a bound that consides every value in the same radical sequence and improves on Lagrange's bound. In this paper, we provide a generalization of Westerfield's bound to the multivariate setting. As a specialization of this bound, we also derive a generalization of Lagrange's bound, which is a strict improvement upon Hong's bound. Finally, we give an algorithm to compute this improved bound. The running time of this algorithm matches the running time of the best known algorithm to compute Hong's bound.
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CASC - A Lower Bound for Computing Lagrange’s Real Root Bound
Computer Algebra in Scientific Computing, 2016Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:In this paper, we study a bound on the real roots of a polynomial by Lagrange. From known results in the literature, it follows that Lagrange’s bound is also a bound on the absolute Positiveness of a polynomial. A simple \(O(n\log n)\) algorithm described in Mehlhorn-Ray (2010) can be used to compute the bound. Our main result is that this is optimal in the real RAM model. Our paper explores the tradeoff between improving the quality of bounds on absolute Positiveness and their computational complexity.
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bounds on absolute Positiveness of multivariate polynomials
Journal of Symbolic Computation, 2010Co-Authors: Prashant Batra, Vikram SharmaAbstract:We propose and study a weighting framework for obtaining bounds on absolute Positiveness of multivariate polynomials. It is shown that a well-known bound B"G by Hong is obtainable in this framework, and w.r.t. any bound in this framework B"G has a multiplicative overestimation which is at most linear in the number of variables. We also propose a general method to algorithmically improve any bound within the framework. In the univariate case, we derive the minimum number of weights necessary to obtain a bound with limited overestimation w.r.t. the absolute Positiveness of the polynomial.
Petr Augusta - One of the best experts on this subject based on the ideXlab platform.
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A numerical test of Positiveness on the unit circle based on the fast Fourier transform
21st Mediterranean Conference on Control and Automation, 2013Co-Authors: Petr AugustaAbstract:The paper presents an algorithm for checking Positiveness of a symmetric polynomial matrix on the unit circle. The algorithm is based on the sampling polynomial matrices using of the fast Fourier transform. The aim of the paper is to show that this approach is significantly faster than commonly used method based on semi-definite programming expression.
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MED - A numerical test of Positiveness on the unit circle based on the fast Fourier transform
21st Mediterranean Conference on Control and Automation, 2013Co-Authors: Petr AugustaAbstract:The paper presents an algorithm for checking Positiveness of a symmetric polynomial matrix on the unit circle. The algorithm is based on the sampling polynomial matrices using of the fast Fourier transform. The aim of the paper is to show that this approach is significantly faster than commonly used method based on semi-definite programming expression.
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A simple method for stabilisation of (2+1)D systems
nDS '13; Proceedings of the 8th International Workshop on Multidimensional Systems, 2013Co-Authors: Petr AugustaAbstract:The paper presents a simple method to stabilise spatially invariant systems described by a parabolic partial differential equation with one temporal and two spatial variables. The method is based on the double use of a technique for the stabilisation of systems with one temporal and one spatial variables. Systems and controllers are described by transfer functions. The stabilisation uses an equivalence of stability of the closed-loop characteristic polynomial and Positiveness of a certain symmetric polynomial matrix. Illustrative examples and numerical simulations are included.
Swaroop N. Prabhakar - One of the best experts on this subject based on the ideXlab platform.
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improved bounds on absolute Positiveness of multivariate polynomials
Journal of Symbolic Computation, 2019Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:Abstract A multivariate polynomial F ( x 1 , x 2 , … , x n ) is said to be absolutely positive from a real number B if F and all its partial derivatives are non-negative for x 1 , x 2 , … , x n ≥ B . One of the well known bounds on absolute Positiveness in the literature is due to Hong. His bound is dependent on the largest number in a certain sequence of radicals defined using the absolute value of the coefficients of the polynomial. In the univariate setting, a bound due to Lagrange considers the first and the second largest numbers in the same radical sequence and is shown by Collins to be better than Hong's bound. In the 1930's, Westerfield had proposed a bound that considers every value in the same radical sequence and improves on Lagrange's bound. In this paper, we provide a hierarchy of bounds generalizing Westerfield's bound to the multivariate setting. One of the bounds in this hierarchy is a generalization of Lagrange's bound. All the bounds are strict quantitative improvements over Hong's bound. We also give an algorithm to compute the multivariate Lagrange bound. The running time of this algorithm matches the running time of the best known algorithm to compute Hong's bound. The algorithm uses the range tree data structure to implement orthogonal range querying. Relying on a result of Fredman (1984), we show that the efficiency of this algorithm cannot be improved by using any other data structure for orthogonal range querying.
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improved bounds on absolute Positiveness of multivariate polynomials
International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:A multivariate polynomial F(x1,x2,...,xn) is said to be absolutely positive from a real number B if F and all its partial derivatives are non-negative for x1,x2,...,xn ≥ B. One of the well known bounds on absolute Positiveness in the literature is due to Hong. His bound is dependent on the first maximum of a certain sequence of radicals defined using the absolute value of the coefficients of the polynomial. In the univariate setting, a bound due to Lagrange considers the first and the second maximum in the same radical sequence and is shown by Collins to be better than Hong's bound. In the 1930's, Westerfield had proposed a bound that consides every value in the same radical sequence and improves on Lagrange's bound. In this paper, we provide a generalization of Westerfield's bound to the multivariate setting. As a specialization of this bound, we also derive a generalization of Lagrange's bound, which is a strict improvement upon Hong's bound. Finally, we give an algorithm to compute this improved bound. The running time of this algorithm matches the running time of the best known algorithm to compute Hong's bound.
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CASC - A Lower Bound for Computing Lagrange’s Real Root Bound
Computer Algebra in Scientific Computing, 2016Co-Authors: Swaroop N. Prabhakar, Vikram SharmaAbstract:In this paper, we study a bound on the real roots of a polynomial by Lagrange. From known results in the literature, it follows that Lagrange’s bound is also a bound on the absolute Positiveness of a polynomial. A simple \(O(n\log n)\) algorithm described in Mehlhorn-Ray (2010) can be used to compute the bound. Our main result is that this is optimal in the real RAM model. Our paper explores the tradeoff between improving the quality of bounds on absolute Positiveness and their computational complexity.
Jiang Ming - One of the best experts on this subject based on the ideXlab platform.
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New result on delay-range-dependent stability analysis for linear system with interval time-varying delay
2015 34th Chinese Control Conference (CCC), 2015Co-Authors: Ge Yuan, Lou Ke, Jiang MingAbstract:This paper focuses on the linear systems with interval time-varying delay, whose lower bound is not restricted to be zero. Through considering the relationship among the time-varying delay, its lower and upper bounds and relaxing the constraint conditions of the determined matrices in Lyapunov-Krasovskii function (LKF), the criterion with a fewer variables is obtained to ensure the Positiveness of LKF and the negativeness of the derivative of LKF. Finally, numerical examples are given to illustrate the effectiveness and the merits of the proposed method.
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Improved delay-range-dependent stability criterion for Markovian jump systems with interval time-varying delay
The 27th Chinese Control and Decision Conference (2015 CCDC), 2015Co-Authors: Lou Ke, Ge Yuan, Jiang MingAbstract:The delay-range-dependent stability problem for Markovian jump systems (MJSs) with interval time-varying is studied in this paper. On the basis of Lyapunov-Krasovskii stability theorem, the variables with the less conservative constraint conditions are used in Lyapunov-Krasovskii functions (LKF) to ensure the Positiveness of the LKF. As a result, some sufficient conditions for stochastic stability are proposed. Finally, two examples are provided to illustrate the merits of the proposed method.