Robust control of piecewise discrete-time linear systems with α-stability constraint

Based on piecewise quadratic Lyapunov function method, this paper first provides stability condition for the autonomous uncertain piecewise discrete-time linear systems, which is a feasibility problem of linear matrix inequalities (LMIs). Then the robust control with a-stability constraint via state feedback controller for uncertain piecewise discrete-time linear systems is presented. It is shown that the controller that minimizing the performance index a can be obtained by solving an optimization problem involving the bilinear matrix inequalities (BMIs).