Stability and stabilization of nonlinear system-Chapter 7非线性系统稳定性和稳定化.pdf

Chapter 7 Applications 7.1 Introduction This chapter aimed to demonstrate the wide applicability of the analysis and syn- thesis tools presented in previous chapters. While there are many good control en- gineering applications we may choose, a tough decision must be made for want of space. We depart from practical application examples commonly adopted by con- trol engineers and researchers, and will study three nonconventional, but challenging and important, case studies from three different areas: mathematical biology, numer- ical analysis, and mathematical economics. These emerging applications are driving forces behind our search for new tools for nonlinear systems and control. The chap- ter objective is to present novel solutions to the feedback stabilization problem by means of the tools presented in previous chapters. In the following, we describe in details these interesting control problems: • The stabilization of a delayed chemostat model (Sect. 7.2). The application shows how the small-gain results of Chap. 5 can be applied for the robust stabilization of uncertain systems with delays. Moreover, the application illustrates the poten- tial of the use of novel small-gain results to difficult problems in Mathematical Biology and process control engineering. • The stabilization of numerical schemes for the numerical solution of systems described by ODEs (Sect. 7.3). This application shows how feedback stabiliza- tion methodologies can be used for the solution of classical problems in areas of applied mathematics different from mathematical control theory. A well-known problem in numerical analysis is converted to an abstract feedback stabilization problem and is solved by applying modern nonlinear feedback design method- ologies. • The stabilization of the price of a commodity by manipulation of buffer stocks (Sect. 7.4). The application shows the efficiency of the proposed feedback