期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 67, 期 5, 页码 2161-2174出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3075763
关键词
Stochastic systems; Power system dynamics; Stability criteria; Lyapunov methods; Stochastic processes; Power system stability; Graph theory; Average dwell-time (ADT) condition; impulsive systems; Lyapunov method; stochastic nonlinear systems
资金
- Natural Science Foundation of Shandong Province [ZR2018MA005, ZR2018MA020, ZR2017MA008]
- Innovation Technology Funding Project in Harbin Institute of Technology [HIT.NSRIF.201703]
This article focuses on the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. The ISS criteria are obtained by constructing a general SISS-Lyapunov function, and the average dwell-time (ADT) condition is imposed for destabilizing impulses and the reverse average dwell-time (RADT) condition for stabilizing impulses. The article also studies the ISS and SISS of impulsive stochastic interconnected systems on networks using the Lyapunov method and graph-theoretic technique.
This article is concerned with the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. By constructing a general SISS-Lyapunov function, which takes the exponential SISS-Lyapunov function as a special case, the ISS criteria are obtained, respectively, for destabilizing and stabilizing impulses. It should be stressed that we impose the average dwell-time (ADT) condition for destabilizing impulses and reverse average dwell-time (RADT) condition for stabilizing impulses to restrain the occurrence of impulses, which extends the fixed dwell-time condition in recent literature. Moreover, the ADT and RADT conditions in this article correspond to the average impulsive interval method in most existing results under the exponential ISS-Lyapunov condition. As a subsequent result, the ISS and SISS of impulsive stochastic interconnected systems on networks are also studied by the Lyapunov method and graph-theoretic technique. Finally, several illustrative examples together with their numerical simulations are provided to demonstrate the theoretical results.
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