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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Non-fragile H 2 and H ∞ filter designs for polytopic two-dimensional systems in Roesser model
TL;DR: The complicated filter design problem is successfully tackled by using the slack variable technique and imposing a structural restriction on the slack matrix.
Journal ArticleDOI
A Riccati equation approach to the design of linear robust controllers
Mao-Lin Ni,Hong-Xin Wu +1 more
TL;DR: By the Lyapunov stability criterion and the Riccati equation, a new procedure for determining a linear control law to stabilize an uncertain system is derived that can be made linear quadratic optimal with respect to an index function for the nominal system.
Proceedings ArticleDOI
Guaranteed cost control of uncertain discrete-time systems with delay in state
TL;DR: In this paper, the authors considered the problem of robust guaranteed cost control of linear discrete timedelay systems with parametric uncertainties and developed a control design method such that the closed-loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays.
Journal ArticleDOI
Robust Root-Clustering of a Matrix in Intersections or Unions of Regions
TL;DR: A method is proposed to compute a bound on the amount of uncertainty ensuring robust root-clustering in a combination (intersection and/or union) of several possibly nonsymmetric half planes, discs, and exteriors of discs.
Proceedings ArticleDOI
Guaranteed cost LQG control of uncertain linear systems
TL;DR: This paper presents a Riccati equation approach to the output feedback quadratic stabilization of uncertain systems that involves the minimisation of a certain bound on an LQG cost function.
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.