Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay |
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Authors: | Zhicheng Li Ming Li Yinliang Xu Hong Huang Satyajayant Misra |
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Affiliation: | 1. School of Electronics and Information Technology (School of Microelectronics), Sun Yat‐sen University, Guangzhou, China;2. Klipsch School of Electrical and Computer Engineering, New Mexico State University, NM, USA;3. Department of Computer Science, New Mexico State University, NM, USA |
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Abstract: | Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method. |
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Keywords: | exponential stochastic stability analysis finite‐time stability analysis semi‐Markovian jump systems stabilization time‐delay systems |
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