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Robust $H\sb{\infty}$ control for linear time-invariant systems with norm-bounded uncertainty in the input matrix. (English) Zbl 0698.93054
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.

93D15Stabilization of systems by feedback
93B50Synthesis problems
93B35Sensitivity (robustness) of control systems
93C05Linear control systems
93C15Control systems governed by ODE
Full Text: DOI
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