Abstract
AbstractIn Chap. 3, we saw how to explicitly construct global, strict Lyapunov functions for time-invariant systems that satisfy Matrosov type conditions. The strict Lyapunov functions were expressed in terms of given nonstrict Lyapunov functions and the auxiliary functions from the Matrosov assumptions. The method relied on a special structure for the upper bounds on the time derivatives of the auxiliary functions. In this chapter, we present a more general strict Lyapunov function construction for time-varying systems, under less stringent Matrosov Conditions. We apply the construction to systems that satisfy time-varying versions of the Jurdjevic-Quinn and LaSalle Conditions. We illustrate our results in a stabilization problem for a time-varying system with a sign constrained controller.KeywordsLyapunov FunctionFunction VersusAuxiliary FunctionUniform Asymptotic StabilityPunov FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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