ROBUST H-INFINITY CONTROL FOR LINEAR TIME-INVARIANT SYSTEMS WITH NORM-BOUNDED UNCERTAINTY IN THE INPUT MATRIX

This paper focuses on the problem of robust H∞ 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∞-norm bound constraint on disturbance attenuation. Paralleling to the theory of robust control, the robust H∞ control problem is solved via the notion of 'quadratic stabilization with an H∞-norm bound constraint'. Necessary and sufficient conditions for quadratic stabilization with an H∞-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∞ optimal control. © 1990.