LPV systems with unstable subsystems: A single Lyapunov function solution to stabilizing switching laws

This investigation presents a synthesis solution for stabilizing switching laws for 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 single Lyapunov function approach and the idea of parameter-dependent Lyapunov functions, a set of linear matrix inequalities guaranteeing the existence of solution. Illustrative examples and the respective simulation results are given that demonstrate the effectiveness of this new synthesis design for this class of LPV systems.