Robust H∞ control for class of uncertain linear time-invariant systems

The problem of robust state feedback H∞ control design for a class of linear time-invariant systems with parameter uncertainty in the state space model is investigated. Uncertain systems with time-invariant norm-bounded parameter uncertainty in the state matrix are considered. A state feedback control design which robustly stabilises the plant and guarantees a robust H∞ performance for the closed-loop system in the face of parameter uncertainty is presented. It is shown that a suitable stabilising feedback law can be constructed in terms of a positive definite solution to a certain parameter-dependent algebraic Riccati equation.