About the book
This book will present the most recent advances in piecewise-smooth continuous systems. It will firstly introduce a classification of hybrid systems, such as impact systems, Filippov and Utkin systems, among others. Based on this classification, the equilibria points and/or limit cycles will be studied, moreover, some aspects regarding bifurcations will be addressed. In the first part of the book, the stability of these systems will be analyzed using different techniques, such as Lyapunov functions and Linear Matrix Inequalities. Later, main aspects of observability are going to be addressed. Special attention will be paid to the joint observability, where both, the continuous and discrete states will be observed by taking advantage of the continuous and discrete structures. The following chapters will deal with the fault diagnosability of hybrid systems. Approaches based on modeled faults will be addressed, where the distinguishability property and the analysis of invariant subspaces are used to guarantee the detection and locations of faults. The second part will focus on the controllability and reachability properties of hybrid systems, and the design of controllers. There are several existing approaches, depending on the class of hybrid system to be considered. The existence of a common Lyapunov function is frequently required for ensuring closed-loop stability; in some particular cases the information of the discrete dynamics is enough to state the stability. The last part will address modelling problems and the applications of the previous results in the design of controllers, observers and diagnosers. Finally, this book intents to provide a general overview regarding the analysis of fundamental properties of piecewise-smooth hybrid systems.