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Stabilization of second-order LTI switched systems XUPING XU{{ and PANOS J. ANTSAKLIS{

Summary: Stabilization of second-order LTI switched systems
This paper studies and solves the problem of asymptotic stabilization of switched systems consisting of unstable second-
order linear time-invariant (LTI) subsystems. Necessary and su cient conditions for asymptotic stabilizability are rst
obtained. If a switched system is asymptotically stabilizable, then the conic switching laws proposed in the paper are used
to construct a switching law that asymptotically stabilizes the system. Switched systems consisting of two subsystems with
unstable foci are studied rst and then the results are extended to switched systems with unstable nodes and saddle points.
The results are applicable to switched systems that consist of more than two subsystems.
1. Introduction
A switched system is a particular kind of hybrid
system that consists of several subsystems and a switch-
ing law specifying the active subsystem at each instant of
time. The interest in switched systems stems from the
fact that many real-world processes and systems in, for
example, chemical, transportation and communication
industries, can be modelled as switched systems (see, e.g.
Morse 1997).
There have already been many results on the stability
analysis of switched systems. Most of the results are
based on Lyapunov's direct method, especially, on the


Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame


Collections: Engineering