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.
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.
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.