Nonlinear systems. Analysis, stability, and control
This book contains the basic techniques and recent results in the analysis, stability and control of nonlinear systems. The treatment is both rigorous and abstract. Some applications are sketched in the exercises. The richness of dynamic behavior predicted by nonlinear differential equations and difference equations is shown in chapter 1. Some important techniques for the analysis of planar continuous and discrete time dynamical systems are presented in chapter 2. Chapter 3 contains a set of mathematical tools for the study of nonlinear systems. Various methods for the input-output analysis are introduced in chapter 4: approximate techniques, input-output methods for stability and Volterra expansions. Chapter 5 is an introduction to the methods of Lyapunov in determining the stability and instability of equilibria of nonlinear systems. Chapter 6 concerns a number of applications of Lyapunov theory: feedback stabilization, the Circle and Popov criteria, adaptive identification, averaging and singular perturbations. In chapter 7, the rudiments of the modern theory of dynamical systems are developed: the Poincaré map and closed orbits, structural stability, bifurcation of vector fields and maps, etc. Some useful background of differential geometry is given in chapter 8. An introduction to input-output linearization by state feedback for continuous time systems is given in chapter 9. In chapter 10, it is shown how to apply the theory of the previous chapter to a number of applications. New directions in nonlinear control and nonholonomy are briefly presented in chapter 11. Some of the important normal forms for exterior differential systems are described in chapter 12. Connections between the exterior differential systems and the vector field approach are also discussed.
scientific article; zbMATH DE number 1325040