Stabilizing switching laws for switched LPV systems with all unstable subsystems

Abstract

Abstract-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 parameterdependent 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.

New result on robust stability of switched systems with all subsystems unstable

“…The existed results of the switched system with all subsystems unstable mainly focused on designing a state‐dependent or time‐dependent switching signal. For state‐dependent switching strategies, the construction of the switching law depends on the full plant state information, which restricts the implementation of the switching rule [21–23]. For the time‐dependent switching, the switching signal is time driven that does not require any information about the system states.…”