Switched and impulsive systems: analysis, design and applications, Zhengguo Li, Yengchai Soh, Changyun Wen; Springer, Berlin. Heidelberg, 2005, ISBN: 3-540-23952-9

The study on hybrid dynamical systems has been attracting increasing attention since 1990s. Generally speaking, a hybrid system is a dynamical system with continuous dynamics, discrete dynamics, and the interaction between them. Hybrid systems are important from both the practical and theoretical points of view. Indeed, hybrid systems naturally represent a wide class of practical systems which are subject to known or unknown abrupt parameter variations, and which undergo sudden change of system structures due to the failure of a component. Another practical motivation for studying hybrid dynamical systems stems from the fact that the hybrid control scheme provides an effective approach for controlling highly nonlinear complex dynamical systems and systems with large uncertainties and/or unknown parameters (Liberzon, 2003; McClamroch & Kolmanovsky, 2000). In fact, as the complexity of the system dynamics increases, it is more and more impractical to design one single controller for achieving desired global performance. It is thus a common practice to design more than one controller, each at a different operating region, and a switching mechanism that coordinates the switching among them. From theoretical viewpoints, the interactions between low-level continuous dynamics and high-level discrete logics, mainly governed by the switching and impulse mechanisms, bring new challenges beyond the conventional system theory (Branicky, Borkar, & Mitter, 1998; Sun & Ge, 2005). The monograph under review provides a timely and comprehensive lecture note on the study of an important class of hybrid systems—the switched and impulsive systems.