Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control - s[Book review; W. M. Haddad; V. S. Chellaboina, and S. G. Nersesov]

An impulsive dynamical system involves interacting continuous-time dynamics and discrete resetting events. Typically, there are three components in an impulsive dynamical system model: a differential equation for its continuous-time dynamics; a difference equation governing the instantaneous changes of the states at the resetting instants; and a criterion for determining when the states of the system are to be reset. Many physical systems in engineering and life science can be treated in the impulsive system framework. The study of impulsive dynamical systems can be traced back at least to the 1980s. Early results on existence of solution, asymptotic properties, stability theory, and other qualitative properties of such systems have been reported in monographs on impulsive differential equations (see, e.g., [4], [6] and the references therein). Unlike these existing monographs, this new book by Haddad et al. adopts a system theoretic approach to impulsive dynamical systems. Instead of laboring on existence of solution and some qualitative properties of such systems, the authors present many interesting results on topics of particular interest to control systems researchers and engineers, such as Lyapunov stability theory, invariant set stability, partial stability, Lagrange stability, boundedness of solutions, dissipativity theory, vector dissipativity theory for large-scale impulsive systems, feedback interconnections, energy-based control and stabilization, optimal control, disturbance rejection control, and robust control. Such a systems perspective on impulsive dynamical systems makes the present book a unique contribution to mathematical control theory. The increasing interest in impulsive dynamical systems is also because of the surging effort in hybrid dynamical systems research by control engineers and computer scientists during the past two decades. A hybrid system is a dynamical system with interacting continuous and discrete (in particular, discrete-event) dynamics. The advent of modern complex engineering systems which contain multiple modes of operation and abstract decision-making units brings into picture many systems simultaneously exhibiting continuous-time dynamics, discrete-time dynamics, logic commands, discrete events, and jumps. To understand and design such complex systems, the analysis and control of hybrid systems need to be thoroughly investigated. There have been many attempts to put together a unified model and framework for hybrid systems. A hybrid system model must successfully address continuous, discrete or discrete-event dynamics, and their interactions. Some prominent attempts for modeling hybrid system can be found in [1]–[3]. However, due to the richness of the behaviors of hybrid systems and diversity of application objectives, a unified modeling framework which can be applied in most cases is still not available. One class of hybrid systems which enjoy a relatively consistent model among researchers is switched systems. A switched system is a