Dissipative Systems

Abstract

In this chapter we will further study the concept of dissipative systems 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 of PR systems to the nonlinear case. Some relationships between Positive Real and Passive systems have been established in Chapter 2. There exist 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 [71], robots with flexible joints [6, 72, 78, 80, 318], underactuated robot manipulators, electric motors, robotic manipulation [25], learning control of manipulators [26,27], fully actuated and underactuated satellites [133], combustion engines [176], power converters [18, 135, 234, 235, 458, 460], neural networks [122, 203, 528, 529], smart actuators [171], piezo-electric structures [269], haptic environments and interfaces [109,128,284,285,289,309,333,422,423,454], particulate processes [131], process and chemical systems [108, 152, 457, 459, 525], missile guidance [283], model helicopters [332], magnetically levitated shafts [355,356], biological and physiological systems [191, 192], flat glass manufacture [526], visual feedback control [252], etc. Some of these examples will be presented in the following chapters.