2008/05/01 by Jun Zhao, David J. Hill · 459 citations
Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Combinatorics #Computer science #Control (management) #Control and Stability of Dynamical Systems #Control theory (sociology) #Discrete mathematics #Electrical engineering #Energy (signal processing) #Engineering #Function (biology) #Mathematics #Passivity #Pure mathematics #Set (abstract data type) #Stability (learning theory) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #State (computer science) #Statistics #Topology (electrical circuits)
paper · open access · doi:10.1109/tac.2008.920237
published in IEEE Transactions on Automatic Control 53(4), 941-953 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2008/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 andL2-gain, are addressed. For both cases, asymptotic stability is guaranteed under certain "negative" output feedback plus asymptotic zero state detectability. Switched passivity conditions and switchedL2-gain inequalities are, respectively, derived, which are generalizations of classical ones. Feedback invariance of passivity and a small-gain theorem are also given.