Model predictive control of uncertain singular systems based on input-to-state stability

In this paper, the problem of input-to-state stability robust model predictive control(MPC) is studied for the discrete time uncertain singular system with input constrain and bounded disturbances. By constructing the ISS-Lyapunov function with the method of linear matrix inequality (LMIs), the “quasi-min-max” optimization problems are converted into finite time convex programming problems. Then the sufficient conditions for the existence of the dual-model robust state feedback predictive controllers are derived. The input-to-state stability of the closed-loop uncertain singular systems is guaranteed by the designed controller. Finally, a numerical simulation is provided to show the application and validity of the proposed method.