Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

Abstract

Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q < 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2,...,2)T. The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.