JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (5): 114-120.doi: 10.6040/j.issn.1671-9352.0.2015.507

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Lyapunov-type stabilizating conditions of discrete-time stochastic systems with input delay

TAN Cheng, ZHANG Huan-shui*   

  1. School of Control Science and Engineering, Jinan 250061, Shandong, China
  • Received:2015-10-30 Online:2016-05-20 Published:2016-05-16

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Abstract: This paper mainly studies the asymptotical mean square stabilization problem for discrete-time stochastic system with single input delay and multiplicative noises. First, expressed by Lyapunov-type inequalities, some sufficient and easily verified stabilizing conditions in mean square sense are developed. Second, based on the derived coupled Lyapunov-type equations(CLEs), a necessary condition is developed. It is remarkable that when the considered stochastic system with input delay degrades into the stochastic system without input delay or the deterministic time-delay system, the reduced system is asymptotical mean square stabilizable if and only if the given CLEs have unique solutions.

Key words: stochastic system, coupled Lyapunov-type equation, input delay, stabilization

CLC Number: 

  • TP13
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