Title :
Dissipativity Theory for Switched Systems
Author :
Zhao, Jun ; Hill, David J.
Author_Institution :
Key Lab. of Integrated Autom. of Process Ind., Northeastern Univ., Shenyang
fDate :
5/1/2008 12:00:00 AM
Abstract :
A framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up. Each subsystem of a switched system is associated with a storage function to describe the "energy" stored in the subsystem, and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active. The exchange of "energy" between the active subsystem and an inactive subsystem is characterized by cross-supply rates. Stability is reached when all supply rates can be made negative, as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense. Two special forms of dissipativity, passivity and L 2 -gain, are addressed. For both cases, asymptotic stability is guaranteed under certain "negative" output feedback plus asymptotic zero state detectability. Switched passivity conditions and switched L 2-gain inequalities are, respectively, derived, which are generalizations of classical ones. Feedback invariance of passivity and a small-gain theorem are also given.
Keywords :
asymptotic stability; time-varying systems; asymptotic stability; cross-supply rates; feedback invariance; multiple storage functions; multiple supply rates; negative output feedback; passivity theorem; small-gain theorem; storage function; switched system dissipativity theory; Asymptotic stability; Australia Council; Automation; Control systems; Energy storage; Laboratories; Lyapunov method; Nonlinear systems; Output feedback; Switched systems; $L_2$-gain; Dissipativity; passivity; stability; switched systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.920237