In the literature, the most comprehensive treatment of stability occurs in the disciplines of physics and control systems. The motivation for defining stability is well stated by Stewart in the foreword of the 1992 translation of A.M. Lyapunov's The General Problem of the Stability of Motion [211] by editor A.T. Fuller. Stewart notes that Lyapunov recognized that there are many distinct concepts of stability different ways to formalize the idea that small disturbances lead to small changes in the motion of a physical body. This general concept has applied to a wide range of disciplines, from engineering to political science. In each case, however, the definition has been adapted to the area to which it is being applied. This chapter will take the same liberties and apply it to complex software and hardware systems. However, it will remain motivated by the concept that small disturbances lead to small changes in the motion.
Chen [212] describes three types of stability in control theory: (1) bounded-input bounded-output; (2) marginal stability; and (3) asymptotic stability. Control theory defines them in terms of differential equations, state-space, and transfer function models.
Bounded-input bounded-output (BIBO) stability is defined as stability where for every bounded input the output is also bounded. A bounded function has a magnitude less than some constant for all time.
Marginal stability is generally referred to as Lyapunov's definition of stability, and...
TABLE OF CONTENTS 
