Discontinuous, and Discrete Systems

Ihave always believed thatstability is the most impor-tant concept in systems and control theory. From the early days of my undergraduate studies, when I was first exposed to Lyapunov theory, to these days in which I devote a significant proportion of time to proving stability properties of dynamical systems and teaching stability to second- and third-year under-graduate students, I have never ceased to be fascinated by the elegance of this notion, its far-reaching implications, and its significance in applications. It is fair to claim that control engineers and mathemati-cians concur in asserting that stability is a property that, in some form, should be possessed by every system, if the sys-tem is to have any practical relevance. For this reason numer-ous research papers, chapters of books, and entire books are devoted to the study of stability, its characterization, descrip-tions of its use in analysis and design, and extensions or vari-ations of the standard notions of Lyapunov and Lagrange. A quick search of the British Library catalo