A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching

• Published in: International journal of robust and nonlinear control Vol. 30; no. 1; pp. 159 - 181
• Main Authors: Chen, Huabin, Shi, Peng, Lim, Cheng‐Chew
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.01.2020
• Subjects: Delay; Hybrid systems; impulsive effect; input‐to‐state stability; Lower bounds; Markovian switching; Perturbation methods; Stability criteria; Switching; time‐varying delay; time‐varying stochastic systems; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4761

Summary In this paper, the problems of the input‐to‐state stability (ISS), the integral input‐to‐state stability (iISS), the stochastic input‐to‐state stability (SISS) and the eλt(λ>0)‐weighted input‐to‐state stability (eλt‐ISS) are investigated for nonlinear time‐varying impulsive stochastic delay systems with Markovian switching. We propose one unified criterion for the stabilizing impulse and the destabilizing impulse to guarantee the ISS, iISS, SISS and eλt‐ISS for such systems. We verify that when the upper bound of the average impulsive interval is given, the stabilizing impulsive effect can stabilize the systems without ISS. We also show that the destabilizing impulsive signal with a given lower bound of the average impulsive interval can preserve the ISS of the systems. In addition, one criterion for guaranteeing the ISS of nonlinear time‐varying stochastic hybrid systems under no impulsive effect is derived. Two examples including one coupled dynamic systems model subject to external random perturbation of the continuous input and impulsive input disturbances are provided to illustrate the effectiveness of the theoretic results developed.