Stabilization of discrete-time switched linear systems under bounded states and controls

The controller synthesis issue for a class of discrete-time switched linear systems via average dwell time switching with bounds on the controls and states is addressed. Firstly, the stabilization problem with sign-restricted controls while imposing positivity and stability on closed-loop system is solved, then the results extend to asymmetrically bounded controls and constrained states. In addition, the bounded control design about systems with polytopic uncertainties is studied. All the derived conditions are formulated as linear programming. Finally, a numerical example is given to show the applicability of the proposed methods.