Dissipative Systems

Abstract

In this chapter we will further study the concept of dissipative system which is a very useful tool in the analysis and synthesis of control laws for linear and nonlinear dynamical systems. One of the key properties of a dissipative dynamical system is that the total energy stored in the system decreases with time. Dissipativeness can be considered as an extension to the nonlinear case of the definition of PR systems. Some relationships between Positive Real and Passive systems have been established in chapter 2. There exists several important subclasses of dissipative nonlinear systems with slightly different properties which are important in the analysis. Dissipativity is useful in stabilizing mechanical systems like fully actuated robots manipulators, robots with flexible joints, underactuated robot manipulators, electric motors, fully actuated and underactuated satellites [49], combustion engines [61], etc.. Some of these examples will be presented in the following chapters.