Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched (gain-scheduled) state feedback control scheme is built to stabilize the constrained time-varying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.