Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Exponential Stabilization of Discrete-Time Switched Linear Systems

Summary: Exponential Stabilization of
Discrete-Time Switched Linear Systems
Wei Zhang a,, Alessandro Abate b
, Jianghai Hu a
, Michael P. Vitus b
Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA
Department of Aeronautics and Astronautics, Stanford University, CA 94305, USA
This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov
function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise
quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis
methods that have adopted piecewise-quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also
proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal
policy of a related switched LQR problem. Motivated by some recent results of the switched LQR problem, an efficient
algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system
is exponentially stabilizable.
Key words: Switched systems, Piecewise quadratic Lyapunov functions, Switching stabilization, Optimal control,
Control-Lyapunov functions.


Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft


Collections: Engineering