Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments

Abstract

In this paper, we establish some criteria on robust exponential stability by using the formula for the variation of parameters and estimating the Cauchy matrix. More importantly, the robust stability criteria do not require the stability of the corresponding continuous system, and so they can be more widely applied to stabilize the unstable continuous system with time delays and uncertainties by using random impulsive control. Further, we give some numerical examples to illustrate the theoretical results.

Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

“…Lemma 1. From [19,28], when there will be exactly m impulses until the time t, t ≥ t 0 , and the waiting time between two consecutive impulses follow exponential distribution with parameter γ, then the probability…”

“…Remark 2. From [19,28], if y(t) is the solution of the random impulsive differential equations, then…”

“…In [18], the author studied the p th moment exponential stability results and the authors [19] discussed the distribution nature for random IDS and proved the exponential stability. For further study, refer to [20][21][22][23][24][25][26][27][28][29] and references therein. Still, now there was no paper reported on the exponential stability for RIIDDS based on the Lyapunov and Razumikhin approach.…”

Approximate controllability of random impulsive quasilinear evolution equation

“…In [2], the author detailed the stabilization nature for random impulsive moments in differential equations with exponential distribution. Recently, in [24,25], the authors investigated the unstable continuous time delay systems controlled by the random impulses and the effects of random impulses shown by the simulation results. Further, the inaccuracy in finding expectation for the solution x(t) of the random impulsive differential systems [3,4,[20][21][22][23] is rectified in this paper.…”

Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

“…Ravi Agarwal, et al [15], proved exponential stability for differential equations with random impulses at random times. For further study refer [10,[16][17][18][19][20][21] and references therein.…”