H ∞ controller design for linear systems with time-invariant uncertainties

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This paper considers the problem of designing robust H ∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H ∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H ∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.