The aim of this paper is to give necessary and sufficient conditions for uniform exponential stability of linear skew-product semiflows on locally compact metric spaces with Banach fibers. Thus, there are obtained generalizations of some theorems due to Datko, Neerven, Clark, Latushkin, Montgomery-Smith, Randolph, van Minh, Räbiger and Schnaubelt.

Fuzzy control systems have had various applications in a wide range of science and engineering in recent years. Since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). Conceptually, there are two types of stability for control systems: Lyapunov stability (a special case ...

It is shown that switching among stable linear systems results in a stable system provided that switching is “slow-on-the-average.” In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all ...

It is shown that switching among stable linear systems results in a stable system provided that switching is “slow-on-the-average.” In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all ...

Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system (e.g., continuous-time dynamics, discrete-time dynamics, jump phenomena, switching and logic commands, and the like) are of great current interest. In the present paper we first formulate a model for hybrid dynamical systems which covers a very large class of systems an...

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For ...