Title: Ultimate Boundedness for Switched Systems with Multiple Equilibria Under Disturbances,
Abstract: In this paper, we investigate the robustness to external disturbances of
switched discrete and continuous systems with multiple equilibria. It is shown
that if each subsystem of the switched system is Input-to-State Stable (ISS),
then under switching signals that satisfy an average dwell-time bound, the
solutions are ultimately bounded within a compact set. Furthermore, the size of
this set varies monotonically with the supremum norm of the disturbance signal.
It is observed that when the subsystems share a common equilibrium, ISS is
recovered for solutions of the corresponding switched system; hence, the
results in this paper are a natural generalization of classical results in
switched systems that exhibit a common equilibrium. Additionally, we provide a
method to analytically compute the average dwell time if each subsystem
possesses a quadratic ISS-Lyapunov function. Our motivation for studying this
class of switched systems arises from certain motion planning problems in
robotics, where primitive motions, each corresponding to an equilibrium point
of a dynamical system, must be composed to realize a task. However, the results
are relevant to a much broader class of applications, in which composition of
different modes of behavior is required.