Stability of State Space Linear Systems

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 23 in State Space and Input-Output Linear Systems, 1998, pp 322-349 from Springer

Abstract: Abstract In this section, we introduce the fundamental definitions and results which lie at the core of stability theory for state space linear systems. We shall see that all of the stability results for state space systems are merely system-theoretic restatements of parallel results for differential equations and difference equations. The stability theory of differential equations is perhaps the most well -developed part of the theory of differential equations as a whole. Over the last century or so, it has occupied the attention of numerous physical scientists and mathematicians; in particular, a great many Soviet mathematicians have made seminal contributions. There is an enormous mathematical literature on stability theory; our attempt will be to provide a fleeting glimpse at the way the theory specializes to linear differential and difference equations.

Keywords: State Space; Difference Equation; Lyapunov Function; Asymptotic Stability; Stable Equilibrium (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3816-4_24

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DOI: 10.1007/978-1-4612-3816-4_24

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