基于H表示的时变随机Markov跳跃系统的能观性
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摘要
研究时变连续和离散随机Markov跳跃系统(SMJSs)的能观性问题.基于H表示方法将时变SMJSs转化为等价的时变线性系统,根据线性系统理论得到时变连续和离散SMJSs的能观性Gramian矩阵判据.数值仿真表明了所得结论的正确性.
The observability of time-varying continuous and discrete-time stochastic Markov jump systems(SMJSs) is investigated. Time-varying SMJSs are transformed into the equivalent time-varying linear systems based on the ?-representation method. Gramian matrix criteria for the observability of time-varying continuous and discrete-time SMJSs are derived based on the linear system theory. A numerical example is given to demonstrate the correctness of the obtained results.
The observability of time-varying continuous and discrete-time stochastic Markov jump systems(SMJSs) is investigated. Time-varying SMJSs are transformed into the equivalent time-varying linear systems based on the ?-representation method. Gramian matrix criteria for the observability of time-varying continuous and discrete-time SMJSs are derived based on the linear system theory. A numerical example is given to demonstrate the correctness of the obtained results.
引文
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[2]Zhang W,Chen B S.On stabilizability and exact observability of stochastic systems with their applications[J].Automatica,2004,40(1):87-94.
[3]Li Z Y,Wang Y,Zhou B,et al.Detectability and observability of discrete-time stochastic systems and their applications[J].Automatica,2009,45(5):1340-1346.
[4]Dragan V,Morozan T,Stoica A M.Mathematical methods in robust control of discrete-time linear stochastic systems[M].New York:Springer,2010:45-48.
[5]Costa E F,Val J B R.On the observability and detectability of continuous-time Markov jump linear systems[J].SIAM J of Control and Optimization,2002,41(4):1295-1314.
[6]Ni Y,Zhang W,Fang H.On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise[J].J of Systems Science&Complexity,2010,23(1):102-115.
[7]Shen L,Sun J,Wu Q.Observability and detectability of discrete-time stochastic systems with Markovian jump[J].Systems&Control Letters,2013,62(1):37-42.
[8]Zhang W,Chen B S.-representation and applications to generalized Lyapunov equations and linear stochastic systems[J].IEEE Trans on Automatic Control,2012,57(12):3009-3022.