Journal ArticleDOI
Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory
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In this paper, the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency domain results on H/sup infinity / optimization.Abstract:
The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H/sup infinity / optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H/sup infinity / control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H/sup infinity / control theory-based methods. >read more
Citations
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Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems
TL;DR: A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix which can be profitably employed also to design a robust feedback stabilization strategy.
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Distributed containment control of fractional-order uncertain multi-agent systems☆
TL;DR: Some sufficient conditions are presented to ensure that the states of the followers can asymptotically converge to the convex hull formed by those of the leaders, and the feedback matrix of the proposed protocol is also determined according to linear matrix inequalities.
Journal ArticleDOI
Optimal guaranteed cost control of 2-D discrete uncertain systems: An LMI approach
Amit Dhawan,Haranath Kar +1 more
TL;DR: A linear matrix inequality (LMI)-based new criterion for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties is established.
Journal ArticleDOI
Multiobjective filter design for uncertain stochastic time-delay systems
A. Subramanian,Ali H. Sayed +1 more
TL;DR: This note addresses the problem of robust multiobjective filtering for discrete time-delay systems with mixed stochastic and deterministic uncertainties, in addition to unmodeled nonlinearities.
Journal ArticleDOI
Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach
TL;DR: In this article, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level y only by employing state-dependent switching rules, which can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance.
References
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State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
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A stabilization algorithm for a class of uncertain linear systems
TL;DR: In this paper, the authors present an algorithm for the stabilization of a class of uncertain linear systems, which is described by state equations which depend on time-varying unknown-but-bounded uncertain parameters.
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Least squares stationary optimal control and the algebraic Riccati equation
TL;DR: In this paper, the optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated, and the integrand of the performance criterion is allowed to be fully quadratically in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem.
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LQG control with an H/sup infinity / performance bound: a Riccati equation approach
TL;DR: In this article, an LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered, and an algorithm is developed for the full-order design problem and illustrative numerical results are given.
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Root locations of an entire polytope of polynomials: It suffices to check the edges
TL;DR: It is shown that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the exposed edges of the polytope.