H ∞ control for time-delay piecewise affine with constrained ellipsoid

This paper dealt with the stabilization problem of a discrete-time piecewise affine (PWA) systems with time-delay. An H∞ state feedback controller design is proposed, and the PWA system was described as ellipsoid which characterized by a set of vector inequalities..thereby the constraint of linear matrix inequalities (LMIs) was released. In terms of LMIs, the time-delay PWA system was stabilized in Lyapunov theory, and the minimum problem of the H∞ performance index can be cast as a convex optimization problem with LMIs constraints. The simulation results verified the effectiveness of the proposed method.