The Experts below are selected from a list of 19278 Experts worldwide ranked by ideXlab platform
Sheng Chen - One of the best experts on this subject based on the ideXlab platform.
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Sparse controller realisation with small roundoff noise
IEE Proceedings - Control Theory and Applications, 2004Co-Authors: Sheng ChenAbstract:In this paper, the effect of roundoff noise in a digital controller is analyzed for a digital feedback control system. An analytical expression for the roundoff noise gain, defined as the ratio between the variances of the output error and the rounding error, is obtained. The problem of identifying the minimum roundoff noise realizations can be solved using an existing procedure. Noting that the optimal realizations are fully parametrized, based on a Polynomial Operator approach a new sparse controller realization is derived. This realization is a generalization of the direct forms in the classical shift Operator and the prevailing delta Operator. It provides us more degrees of freedom to reduce the roundoff noise. The problem of finding optimal Polynomial Operators can be solved with exhaustive search, and a design example is given. It is shown that with the proposed sparse realization the optimal Polynomial Operators can outperform the shift- and delta-Operators.
J.x. Hao - One of the best experts on this subject based on the ideXlab platform.
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ICARCV - Polynomial Operator-based digital controller structures of high stability performance and computation efficiency
ICARCV 2004 8th Control Automation Robotics and Vision Conference 2004., 1Co-Authors: J.x. HaoAbstract:In this paper, the optimal controller structure problem is investigated with finite word length (FWL) consideration. Based on the Polynomial Operator concept, a new sparse controller structure is proposed. This structure is efficient in terms of implementation and can be optimized to reduce FWL effects. A pole modulus sensitivity based stability measure is derived and the optimal controller structures are defined as those that maximize the proposed measure. The problem of finding optimal sparse structures is solved using exhaustive searching with a practical consideration. A design example is given, which shows that the newly developed structure can beat the fully parametrized optimal state-space realization in terms of both computation efficiency and stability performance.
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ISCAS (4) - A generalized direct-form II transposed structure for IIR filter implementation with minimal roundoff noise gain
Proceedings of the 2003 International Symposium on Circuits and Systems 2003. ISCAS '03., 1Co-Authors: Z.x. Zhao, J.x. HaoAbstract:In this paper, based on a Polynomial Operator approach a new structure is derived. This structure is a generalization of the direct-form II transposed structures in the conventional shift-Operator and the prevailing delta-Operator. The use of Polynomial Operators provides more degrees of freedom for minimizing the roundoff noise gain of the structure without increasing the computation complexity. Numerical examples are presented to illustrate the design procedure. It is shown that the optimized Polynomial Operators can yield a much better performance than the shift and delta Operators.
J. Hao - One of the best experts on this subject based on the ideXlab platform.
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Polynomial Operator based sparse controller structures with stability consideration
IEE Proceedings - Control Theory and Applications, 2005Co-Authors: J. HaoAbstract:Two new efficient controller structures are derived based on a Polynomial Operator approach. The first one can be considered as an improved version of the recently proposed direct-form II transposed (DFIIt) structure in the ρ-Operator, in which the first-order ρ-Operators are replaced with a set of second-order Operators, while the second one is the equivalent state-space realisation. A pole modulus sensitivity based stability measure is obtained and the corresponding expression of the stability robustness for each structure is derived. The optimal structure problem is solved by maximising the stability robustness under the parameter dynamical range constraints for fixed-point implementations. A design example is given, which shows that the newly developed structures can achieve much better stability performance than those structures in first-order ρ-Operators and furthermore, outperform the fully parametrised optimal realisation in terms of both stability robustness and implementation efficiency.
Christian Engstrom - One of the best experts on this subject based on the ideXlab platform.
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on the spectrum of a holomorphic Operator valued function with applications to absorptive photonic crystals
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: Christian EngstromAbstract:We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic Operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational Operator-valued function in terms of a Polynomial Operator pencil and study two-component dispersive and absorptive crystals in detail.
Lingzhong Zeng - One of the best experts on this subject based on the ideXlab platform.
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Estimates for lower bounds of eigenvalues of the poly-Laplacian and the quadratic Polynomial Operator of the Laplacian
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013Co-Authors: Qing-ming Cheng, Hejun Sun, Guoxin Wei, Lingzhong ZengAbstract:In this paper, we investigate the Dirichlet eigenvalue problems of the poly-Laplacian with any order and the quadratic Polynomial Operator of the Laplacian. We give some estimates for lower bounds of the sums of their first k eigenvalues.
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The Eigenvalue Problems on Riemannian Manifolds
2013Co-Authors: Lingzhong ZengAbstract:In this thesis, we mainly study eigenvalues of the following five eigenvalue problems in various settings: the Dirichlet eigenvalue problem of the Laplacian; the Dirichlet eigenvalue problem of the poly-Laplacian; the Dirichlet eigenvalue problem of the quadratic Polynomial Operator; the eigenvalue problem of the poly-Laplacian; and the closed eigenvalue problem of Witten-Laplacian. In Chapter 2, we present the basic definitions and facts to be used in the subsequent chapters. Few proofs are presented here. For the Dirichlet eigenvalue problem of the poly-Laplacian on bounded domains in an n- dimensional Euclidean space Rn, we mainly focus our attention on the investigation for lower bounds of the sum of eigenvalues. For one thing, for the case of l = 1, we obtain a sharper lower bound for the sum of its eigenvalues in chapter 3, which gives an improvement of results due to Melas (Proc. Amer. Math. Soc. 131 (2003), 631-636.). However, for the case of poly-Laplacian with arbitrary order, we also yield a lower bound for eigenvalues, which generalizes the results due to Cheng-Wei (to appear in J. Diff. Equa.) and gives an improvement of results due to Cheng-Qi- Wei (to appear in Pacific J. Math.). On the other hand, we also discuss the Dirichlet eigenvalue problem of the quadratic Polynomial Operator and give some estimates for lower bounds of the sums of their first k-eigenvalues. Furthermore, by the method of approximation of function, we improve the previous results in term of the term associated with coefficient of k 2l−2 n . In the remainder of the chapter, we investigate the eigenvalue problem of the fractional Laplacian (−∆)|Ω, where α ∈ (0, 2], and obtain a sharper lower bound for the sum of its eigenvalues, which gives an improvement of results due to Yolcu-Yolcu (to appear in Communications in Contemporary Math.). In Chapter 4, we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an n-dimensional compact Riemannian manifold. Estimates for eigenvalues are given. As applications, we give a sharp upper bound for the k-th eigenvalue and for isoparametric minimal i ii hypersurfaces in the unit sphere, an explicit upper bound of the (n + 3)-th eigenvalue of the Laplacian is obtained. Furthermore, we generalize the Reilly’s result on the first eigenvalue of the Laplacian. The final chapter is continuous to consider the Dirichlet problem of poly-Laplacian with ar- bitrary order on a bounded domain in a complete Riemannian manifold. To begin with, we establish an abstract inequality for lower order eigenvalues of a self-adjoint Operator on a Hilbert space which generalizes and extends the recent results of Cheng-Huang-Wei (Calc. Var. Part. Diff. Equa., 38, 409-416 (2010)). Then, making use of it, we obtain some universal inequalities for lower order eigenvalues of the biharmonic Operator on manifolds admitting some special func- tions. Moreover, we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space.
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Estimates for lower bounds of eigenvalues of the poly-Laplacian and quadratic Polynomial Operator of the Laplacian
arXiv: Differential Geometry, 2011Co-Authors: Qing-ming Cheng, Hejun Sun, Guoxin Wei, Lingzhong ZengAbstract:In this paper, we investigate the Dirchlet eigenvalue problems of poly-Laplacian with any order and quadratic Polynomial Operator of the Laplacian. We give some estimates for lower bounds of the sums of their first $k$ eigenvalues which improve the previous results.