Stabilization and Guaranteed Cost Control of Discrete-Time Singular Piecewise-Affine Systems with Time Delay

This paper is concerned with the problem of designing output feedback controller and guaranteed cost controller of discrete-time singular piecewise-affine systems with time delay and norm-bounded time-varying parameters uncertainties. Firstly, the corresponding operating region of the time-delay singular piecewise-affine systems in state space is described as ellipsoid which can be solved by a set of vector inequalities. Then, based on a singular piecewise Lyapunov-Krasovskii function combined with S-procedure and some matrix inequality convexifying techniques, the output feedback controller of the time-delay singular systems is investigated, and meanwhile, the guaranteed cost controller of the time-delay singular piecewise-affine systems is solved in terms of linear matrix inequalities (LMIs). It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Numerical examples are given to illustrate the effectiveness of the proposed design methods. Moreover, it is suitable for practical application.