I -Eventual Stability of Differential Systems with Impulses
Ψ -eventual stability, Ψ -uniform eventual stability, impulsive differential systems, lyapunov’s function
Abstract
In our paper, we have established criterion of Ψ-Eventual Stability for impulsive differential systems with variable moments of impulses by using piecewise continuous auxiliary functions which are analogous to Lyapunov's functions. The work of Bainov, Kulev and Soliman has been extended. An example has been given to support the theoretical result. In the example, the zero solution is not stable in the sense of Lyapunov but it is uniformly eventually stable. Moreover a weight function Ψ is also associated with state vectors.
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References
G Kulev, D Bainov (1988) Asymptotic stability of systems with impulses by the direct method of Lyapunov. 38(1), 113-123.
Diamandescu (2005) On the Ψ-stability of a nonlinear volterra integro differential systems. 56, 1-14.
Aurel Diamandescu (2008) On the ψ-exponential asymptotic stability of nonlinear systems of differential equations. 58(2), 293-306.
J Morchalo (1990) On (Ψ-Lp) stability of nonlinear systems of differential equations. 4, 353-360.
A Soliman (2003) Stability criteria of impulsive differential systems. 134, 445-457.
Anju Sood, S Srivastava (2012) New conditions for stability of solution of impulsive differential equations. 6(86), 4295-4300.
Yu Zhang, Jitao Sun (2007) Eventual stability of impulsive differential systems. 27(2), 373-380.
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2014-10-29
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