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A new unified input‐to‐state stability criterion for impulsive stochastic delay systems with Markovian switching
Author(s) -
Chen Huabin,
Shi Peng,
Lim ChengChew
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4761
Subject(s) - control theory (sociology) , impulse (physics) , nonlinear system , perturbation (astronomy) , upper and lower bounds , stability (learning theory) , mathematics , interval (graph theory) , state (computer science) , markov process , stability criterion , computer science , algorithm , physics , discrete time and continuous time , mathematical analysis , control (management) , statistics , quantum mechanics , combinatorics , artificial intelligence , machine learning
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 e λ t ( λ >0)‐weighted input‐to‐state stability ( e λ t ‐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 e λ t ‐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.