 
Summary: Characterizing Uniformly Ultimately Bounded Switching Signals for
Uncertain Switched Linear Systems
Hai Lin and Panos J. Antsaklis
Abstract In this paper, the uniformly ultimately bounded
(UUB) switching control problem is investigated for a class
of continuoustime switched linear systems with parametric
uncertainties and exterior disturbances. It is assumed that each
subsystem is UUB. First, a class of switching signals, which may
contains infinite number of switching and preserves the UUB of
the switched systems, is characterized. Then, a switching law is
synthesized to improve the disturbance attenuation properties
in the sense that all state trajectories can converge into a smaller
region than any single subsystem acts alone. The switching law
is given as a static state feedback form, and provides a conic
partition of the state space. To avoid unstable sliding motions,
some modifications are introduced later. The techniques are
based on multiple polyhedral Lyapunov functions.
I. INTRODUCTION
A switched system is a dynamical system that consists
of a finite number of subsystems described by differential
