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L1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

Wenhai Qi* and Xianwen Gao
International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp.274-280, 2017

Abstract : "This paper deals with the problem of L1 control for positive Markovian jump systems with partly known transition rates. First, by constructing an appropriate linear co-positive type Lyapunov-Krasovskii function, stochastic stability for the underlying system is discussed. Then, the L1-gain performance is analyzed. Based on the results obtained, an effective method is proposed for the design of state feedback controller. All the proposed conditions are derived to ensure that the closed-loop Markovian jump system positive and stochastically stable with L1-gain performance in linear programming. Finally, an example is given to demonstrate the validity of the main results."

Keyword : Linear programming, partly known transition rates, positive Markovian jump systems, stochastic stability.

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