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

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
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### References:

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