An Extension of Barbashin-Krasovski-LaSalle Theorem to a Class of Nonautonomous Systems
نویسنده
چکیده
In this paper we give an extension of Barbashin-Krasovski-LaSalle Theorem to a class of timevarying dynamical systems, namely the class of systems for which the restricted vector eld to the zero-set of the time derivative of the Liapunov function is time invariant and this set includes some trajectories. Our goal is to improve the su cient conditions for the case of uniform asymptotic stability of the equilibrium. We obtain an extension of an well-known linear result to the case of zero-state detectability (given (C;A) a detectable pair, if there exists a positive semide nite matrix P 0 such that: AP + PA+CC = 0 then A is Hurwitz -i.e. it has all eigenvalues with negative real part) as well as a result about robust stabilizability of nonlinear a ne control systems.
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