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Zbl 0698.93054
Xie, Lihua; de Souza, Carlos E.
Robust $H\sb{\infty}$ control for linear time-invariant systems with norm-bounded uncertainty in the input matrix. (English)
[J] Syst. Control Lett. 14, No.5, 389-396 (1990). ISSN 0167-6911

Summary: This paper focuses on the problem of robust $H\sb{\infty}$ control design for a class of linear time-invariant systems with uncertainty in the state space model. We consider uncertain systems with norm-bounded parameter uncertainty in the input matrix. The paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an $H\sb{\infty}$-norm bound constraint on disturbance attenuation. Paralleling to the theory of robust control, the robust $H\sb{\infty}$ control problem is solved via the notion of `quadratic stabilization with an $H\sb{\infty}$-norm bound constraint'. Necessary and sufficient conditions for quadratic stabilization with an $H\sb{\infty}$-norm bound are derived. It is shown that the solution to this problem involves solving a parameter-dependent algebraic Riccati equation. The results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and $H\sb{\infty}$ optimal control.

MSC 2000:: *93D15 Stabilization of systems by feedback
93B50 Synthesis problems
93B35 Sensitivity (robustness) of control systems
93C05 Linear control systems
93C15 Control systems governed by ODE

Keywords: robust $H\sb{\infty}$ control design; norm-bounded parameter uncertainty; state feedback control; quadratic stabilization; algebraic Riccati equation; time-invariant

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Zentralblatt MATH Berlin [Germany]