Stability of Dissipative Systems

Abstract

In this chapter, various results concerning the stability of dissipative systems are presented. First, the input/output properties of several feedback interconnections of passive, negative imaginary, maximal monotone systems are reviewed. Large-scale systems are briefly treated. Then the conditions under which storage functions are Lyapunov functions are given in detail. Results on stabilization, equivalence to a passive system, input-to-state stability, and passivity of linear delay systems are then provided. The chapter ends with an introduction to $$H:{\infty }$$ theory for nonlinear systems that is related to a specific dissipativity property, and with a section on Popov’s hyperstability.