Stabilizing switching laws for switched LPV systems with all unstable subsystems

This investigation presents a synthesis solution for stabilizing switching laws a class of parameter-varying plants represented via linear LPV systems that has all unstable subsystems. Considered class of LPV systems has state matrices as parametrically affine with parameter varying in a convex set for which all the subsystems are unstable. Stabilization design of switching laws is solved that enforce overall state trajectory that is asymptotically convergent to the equilibrium state. Via the parameter-dependent multiple Lyapunov function approach, a set of linear matrix inequalities guaranteeing the existence of parameter-dependent Lyapunov functions is derived. An illustrative example and the respective simulation results are given that demonstrate the effectiveness of this new synthesis design for this class of LPV systems.