On Stability in Impulsive Dynamical Systems

Krzysztof Ciesielski

Displaying similar documents to “On Stability in Impulsive Dynamical Systems”

Converse theorem for practical stability of nonlinear impulsive systems and applications

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The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main...

Strict stability criteria for impulsive functional differential systems.

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Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method

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We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.

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Global exponential stability of impulsive functional differential equations via Razumikhin technique.

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On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown...