Modern Control System Theory and Design, 2nd Edition

5.2.  STABILITY

The degree of stability is an extremely important part of describing a control system’s performance criteria. It is a very complex subject, and five chapters are devoted to it. In Chapter 6 we address the question of whether a linear system is stable or not. If it is stable, we determine how stable it is. If it is unstable, we determine how unstable it is. No effort is made in Chapter 6 to make an unstable system stable, or improve the stability or a marginally stable system. That is reserved for Chapters 7 and 8, where we design linear control systems and make the systems meet the stability specifications required. The question of stability of nonlinear control systems is addressed in the accompanying volume, where we extend the technique of linear system stability analysis and design to nonlinear systems. The stability of digital control systems is also presented there. The design of control systems to meet required stability specifications is further illustrated in Chapter 7 of the accompanying volume, where case studies of control-system designs are presented.

In this chapter, linear system stability is briefly addressed in this section to focus attention on its importance in the overall concept of control-system performance criteria considerations. A feedback control system must be stable even when the system is subjected to command signals, extraneous inputs anywhere within the loop, power-supply variations, and changes in parameters of the feedback loop. ...