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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Robust H/sub 2//H/sub /spl infin//-state estimation for discrete-time systems with error variance constraints
TL;DR: The problem addressed is the design of a gain-scheduled linear state estimator such that the variance of the estimation error of each state is not more than the individual prespecification value, and the transfer function from disturbances to error state outputs satisfies the prespecified H/sub /spl infin//-norm upper bound constraint, simultaneously.
Journal ArticleDOI
Robust stabilization of nonlinear systems with pointwise norm-bounded uncertainties: a control Lyapunov function approach
TL;DR: The approach, based on Lyapunov functions, generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization, on one hand, and H/sub /spl infin//-control sector conditions and input-to-state stabilization on the other.
Journal ArticleDOI
Motion Tracking Control Design for a Class of Nonholonomic Mobile Robot Systems
TL;DR: Motion tracking control design of nonholonomic mobile robot systems considering actuator dynamics is addressed and a numerical example is shown to demonstrate and validate the proposed approach.
Journal ArticleDOI
Robust saturation controller for linear time-invariant system with structured real parameter uncertainties
TL;DR: In this paper, a robust saturation controller for the linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties is proposed, which can analytically prescribe the upper and lower bounds of parameter uncertainties, and guarantee the closed-loop robust stability of the system in the presence of actuator saturation.
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Petersen's lemma on matrix uncertainty and its generalizations
TL;DR: In this paper, various generalizations and refinements are proposed for a well-known result on robust matrix signdefiniteness, which is extensively exploited in quadratic stability, design of robustly quadratically stabilizing controllers, robust LQR-problem, etc.
References
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Journal ArticleDOI
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.