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New inclusion criterion for the stability of interval matrices

IEE PROCEEDINGS-CONTROL theory AND applications 2006年第4期153卷 478-482页

作者： Franze, G. Carotenuto, L. Balestrino, A. Univ Calabria DEIS I-87036 Arcavacata Di Rende CS Italy Univ Pisa Dipartimento Sistemi Elettr & Automaz I-56127 Pisa Italy

New results on the regions that include the spectrum of a given matrix have recently appeared in the literature. On the basis of the inclusions established, a new method is proposed for analysing the stability of a class of uncertain linear systems characterised by an interval family of dynamical matrices. As a result, a new bound to the real parts (moduli) of the eigenvalues of matrices in the interval family is obtained, which provides a sufficient condition of stability and a way to compute an estimate of the minimal destabilising perturbation (stability margin). The evaluation of this bound, as well as of other ones obtained by Gersgorin regions, is computationally simple and does not suffer from dimensionality problems. Then, the method can be used also when less conservative approaches (exploration of vertices and joining segments) require prohibitive computational efforts. Moreover, numerical comparisons, carried out on a large number of randomly generated interval matrices, show that the bound proposed here is inferior in about 3% and superior in about 25% in comparison to the results of a recently published Gersgorin-type method (Carotenuto et al., 2004).

关键词： algebra Gersgorin regions inclusion criterion uncertain linear systems uncertain systems dynamical matrices linear systems eigenvalues and eigenfunctions Stability in control theory eigenvalues stability matrix algebra Control system analysis and synthesis methods state-space methods interval matrix stability

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Robust stability of uncertain time-varying state-delayed systems

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第4期153卷 469-477页

作者： Parlakci, M. N. A. Istanbul Bilgi Univ Dept Comp Sci TR-34440 Istanbul Turkey

Robust stability for uncertain systems with time-varying delay is investigated. An improved linear matrix inequality-based robust delay-dependent stability test is introduced to ensure a larger upper bound for time-varying delays affecting the state vector of an uncertain continuous-time system with norm-bounded type uncertainties. A new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation is constructed to derive some delay-dependent stability criteria. The proposed method gives sufficient conditions for the robust stability of the system with time-varying delay under norm-bounded uncertainty. numerical examples indicate that the proposed stability criteria effectively improve the existing results.

关键词： delays linear matrix inequality linear matrix inequalities Lyapunov-Krasovskii functionals Distributed parameter control systems stability criteria continuous-time system Lyapunov methods algebra continuous time systems time-varying delay uncertain system robust stability robust delay dependent stability test norm bounded uncertainty uncertain systems time-varying systems robust control Stability in control theory Time-varying control systems

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Lie algebra representations, nilpotent matrices, and the C-numerical range

Lie algebra representations, nilpotent matrices, and the <i>...

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11th conference of the International-linear-algebra-Society

作者： Dirr, G Helmke, U Kleinsteuber, M Univ Wurzburg Math Inst D-97074 Wurzburg Germany

In this paper we survey some applications of the representation theory of Lie algebras to linear algebra. This includes the derivation of the Jordan form for tensor products of invertible matrices, the study of normal form problems for nilpotent matrices, as well as the derivation of explicit formulas for the C-numerical radius of certain nilpotent block-shift matrices, arising in quantum mechanics and nuclear magnetic resonance (NMR-) spectroscopy. In this latter case, a conjecture concerning an explicit formula for the C-numerical radius is stated. We show the existence of unitary transformations that realize the prospective maxima. Our approach depends on the Clebsch-Gordan decomposition for unitary representations of su(2)(C). (c) 2005 Elsevier Inc. All rights reserved.

关键词： Lie algebra representations Clebsch-Gordan decomposition Nilpotent matrices C-numerical range NMR-spectroscopy

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LMI-based criteria for globally robust stability of delayed Cohen-Grossberg neural networks

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第4期153卷 397-402页

作者： Wang, W. Cao, J. SE Univ Dept Math Nanjing 210096 Peoples R China

The issue of globally robust asymptotic stability with norm-bounded parameter uncertainties is studied for delayed Cohen-Grossberg neural networks. By constructing a suitable Lyapunov functional, several sufficient conditions are obtained guaranteeing the global robust convergence of the equilibrium point. The obtained conditions are given in the form of matrix and linear matrix inequalities that can be checked numerically and very efficiently by resorting to the recently developed interior-point method. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the obtained results.

关键词： uncertain systems linear matrix inequalities global robust convergence robust asymptotic stability asymptotic stability Lyapunov functional delays interior-point method Neural nets Lyapunov methods algebra delayed Cohen-Grossberg neural networks

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Note on finite eigenvalues of regular descriptor systems

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第4期153卷 502-503页

作者： Bavafa-Toosi, Y. Ohmori, H. Labibi, B. Keio Univ Grad Sch Sci & Technol Sch Integrated Design Engn Kohoku Ku Kanagawa 2238522 Japan KN Toosi Univ Technol Dept Elect Engn Tehran Iran

A necessary and sufficient condition is presented for the finite spectrum of a regular descriptor system to lie within a certain region of the complex s-plane.

关键词： linear algebra (numerical analysis) complex s-plane finite eigenvalues eigenvalues and eigenfunctions regular descriptor systems Control system analysis and synthesis methods pole assignment

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Delay-dependent guaranteed cost control for uncertain systems with state and input delays

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第3期153卷 307-313页

作者： Xu, S. Lam, J. Zou, Y. Nanjing Univ Sci & Technol Dept Automat Nanjing 210094 Peoples R China Univ Hong Kong Dept Mech Engn Hong Kong Hong Kong Peoples R China

The authors deal with the problem of delay-dependent guaranteed cost control for uncertain linear systems with time-varying delays in both the state and the input. The purpose of this is to design state-feedback controllers such that the resulting closed-loop system is robustly stable, and a specified linear integral-quadratic cost function has an upper bound for all delays in the given intervals. Two types of the time-varying delays are considered. Delay-dependent sufficient conditions for the solvability of the problem are developed in terms of matrix inequalities. By the cone complementary linearisation method, desired state-feedback controllers can be constructed. A numerical example is provided to demonstrate the applicability of the proposed method.

关键词： state-feedback controller design uncertain linear systems delay-dependent guaranteed cost control state feedback linear matrix inequalities Distributed parameter control systems matrix inequalities linear systems algebra control system synthesis linearisation techniques closed loop systems time-varying delays Control system analysis and synthesis methods complementary linearisation method uncertain systems input delays closed loop system time-varying systems delay systems Time-varying control systems

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Positive cones and convergence conditions for iterative methods based on splittings

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linear algebra AND ITS applications 2006年第2-3期413卷 319-326页

作者： Climent, JJ Herranz, V Perea, C Univ Alicante Dept Ciencia Comput & Intelligencia Artificial E-03080 Alicante Spain Univ Miguel Hernandez Dept Estadist & Matemat Aplicada Ctr Invest Operat E-03202 Elche Spain Univ Miguel Hernandez Dept Estadist & Matemat Aplicada Ctr Invest Operat EPSO E-03312 Orihuela Spain

The study of convergence conditions to solve large and sparse linear systems Ax = b by iterative methods has been discussed by many authors. In this paper, by using the partial order induced by positivity cone of matrices and conditions on the matrices and splittings, we obtain the convergence of the iterative method. The usual partial orders of nonnegative matrices and nonnegative definite matrices satisfy the conditions presented for this new order, and hence, we unify the theory. Moreover, we also show that the new conditions apply to other partial orders as well, thus extending the usual convergence theory to a new situation. (c) 2005 Elsevier Inc. All rights reserved.

关键词： linear system positivity cone partial order splitting convergence result

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Delay-dependent robust H_∞ and L₂-L_∞ filtering for LPV systems with both discrete and distributed delays

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第4期153卷 483-492页

作者： Wu, L. Shi, P. Wang, C. Gao, H. Harbin Inst Technol Space Control & Inertial Technol Res Ctr Harbin 150001 Peoples R China Univ Glamorgan Sch Technol Pontypridd CF37 1DL M Glam Wales Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2M7 Canada

The problems of delay-dependent robust H-infinity and L-2-L-infinity filtering for a class of linear parameter varying systems with both discrete and distributed delays is discussed. The distributed delays are assumed to appear in both the state and measurement equations. Attention is focused on the design of delay-dependent robust full-order filters that guarantee the robust asymptotic stability and a prescribed noise attenuation level in an H-infinity or L-2-L-infinity sense for the filtering error dynamics. The desired filters can be obtained from the solution of convex optimisation problems in terms of linear matrix inequalities that can be solved by efficient interior-point algorithms. A numerical example is included to illustrate the effectiveness of the proposed design methods.

关键词： robust asymptotic stability asymptotic stability distributed delays linear matrix inequalities Distributed parameter control systems H∞ control delay dependent robust H∞ filtering Optimal control linear parameter varying system algebra linear systems discrete delays convex optimization filtering theory filtering error dynamics L2-L∞ filtering delay systems robust control Stability in control theory interior point algorithms Signal processing theory

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New subclasses of block H-matrices with applications to parallel decomposition-type relaxation methods

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numerical ALGORITHMS 2006年第3-4期42卷 325-334页

作者： Cvetkovic, Ljiljana Kostic, Vladimir Univ Novi Sad Fac Sci Dept Math & Informat Novi Sad 21000 Serbia

The parallel decomposition-type relaxation methods for solving large sparse systems of linear equations on SIMD multiprocessor systems have been proposed in [3] and [2]. In case when the coefficient matrix of the linear system is a block H-matrix, sufficient conditions for the convergence of methods given in [2], [3] have been further improved in [5] and [4]. From the practical point of view, the convergence area obtained there is not always suitable for computation, so we propose new, easily computable ones, for some special subclasses of block H-matrices. Furthermore, this approach improves the already known convergence area for the class of block strictly diagonally dominant (SDD) matrices.

关键词： relaxation methods parallel decomposition block H-matrices

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Discrete fuzzy control of time-delay affine Takagi-Sugeno fuzzy models with H_∞ constraint

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IEE PROCEEDINGS-CONTROL theory AND applications 2006年第6期153卷 745-752页

作者： Chang, W. J. Chang, W. Natl Taiwan Ocean Univ Dept Marine Engn Chilung 202 Taiwan

Takagi-Sugeno (T-S) fuzzy models play an important role in nonlinear control because they can be used to approximate nonlinear systems. Also, for the affine T-S fuzzy models, the local linear sub-system properties can be easily related to the physics of the controlled nonlinear system. This is one advantage of the affine T-S fuzzy models relative to the homogeneous T-S fuzzy models. In the literature, however, most authors have focused on the homogeneous T-S fuzzy models and only a few have considered the affine T-S fuzzy models. Moreover, it is known that time delays exist in physical systems. To date, there has been no study to consider the time-delay effects in the analysis of affine T-S fuzzy models. Therefore the parallel distributed compensation-based H-infinity fuzzy control problem for the discrete time-delay affine T-S fuzzy model is now presented. An iterative linear matrix inequality algorithm is used to solve the bilinear matrix inequality problems. Finally, numerical simulation for a time-delayed nonlinear truck-trailer system is given to show an application of the present approach.

关键词： iterative linear matrix inequality fuzzy control discrete fuzzy control bilinear matrix inequality linear matrix inequalities Distributed parameter control systems H∞ constraint H∞ control nonlinear control systems Optimal control Takagi-Sugeno fuzzy model nonlinear control algebra Nonlinear control systems Interpolation and function approximation (numerical analysis) Discrete control systems Fuzzy control iterative methods time-delay affine model delay systems parallel distributed compensation discrete systems

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