New upper solution bounds for perturbed continuous algebraic Riccati equations applied to automatic control. (English) Zbl 1143.93336

Davies, Richard; Shi, Peng; Wiltshire, Ron

Chaos Solitons Fractals 32, No. 2, 487-495 (2007).

Summary: In dynamical systems studies, the so-called Riccati and Lyapunov equations play an important role in stability analysis, optimal control and filtering design. In this paper, upper matrix bounds for the perturbation of the stabilizing solution of the continuous algebraic Riccati equation are derived for the case when one, or all the coefficient matrices are subject to small perturbations. Comparing with existing works on this topic, the proposed bounds are less restrictive. In addition to these bounds, iterative algorithms are also derived to obtain more precise estimates.

MSC:

93D21	Adaptive or robust stabilization
93C05	Linear systems in control theory
93C70	Time-scale analysis and singular perturbations in control/observation systems

Keywords:

Riccati and Lyapunov equations; stability analysis; bounds of small perturbations

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