Brief Review of Dissipativity Theory

This chapter reviews concepts from dissipativity theory that are foundational for the subsequent chapters. It first gives the general definition and, next, discusses special types of dissipativity that describe finite \(L_2\) gain, passivity, and output strict passivity properties, followed by a graphical interpretation of each type for memoryless systems. The next topic is differential characterization of dissipativity and its specialization to linear systems. This is followed by numerical techniques for certifying dissipativity via semidefinite programming. The final section illustrates the use of dissipativity for reachability and Lyapunov stability analysis.