Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria
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This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since—after establishing the invariance of observability under output injection—this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.
Key wordsControl systems Differential equations Time-variance Observability Asymptotic stability Circle criterion
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