Vector lyapunov functions

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  • Modern complex dynamical systems1 are highly interconnected and mutually interdependent, both physically and through a multitude of information and communication network constraints. The sheer size (i.e., dimensionality) and complexity of these large-scale dynamical systems often necessitates a hierarchical decentralized architecture for analyzing and controlling these systems. Specifically, in the analysis and control-system design of complex large-scale dynamical systems it is often desirable to treat the overall system as a collection of interconnected subsystems.

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  • T he impetus to produce this book came in a brief phone call in 1998. Chuck Crumly, of Academic Press, called with an invitation and a deadline. Either The Ecology of Fishes on Coral Reefs, published in 1991, would be allowed to lapse into out-of-print status, or I would agree to produce a second edition. Looking back on all the work, I suspect it might have been wiser to say, "Let her lapse." But I didn't.

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  • EXPONENTIAL STABILITY OF DYNAMIC EQUATIONS ON TIME SCALES ALLAN C. PETERSON AND YOUSSEF N. RAFFOUL Received 6 July 2004 and in revised form 16 December 2004 We investigate the exponential stability of the zero solution to a system of dynamic equations on time scales. We do this by defining appropriate Lyapunov-type functions and then formulate certain inequalities on these functions. Several examples are given. 1. Introduction This paper considers the exponential stability of the zero solution of the first-order vector dynamic equation x∆ = f (t,x), t ≥ 0. (1.

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