Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 55, Issue 7, Pages 1656-1662Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2046114
Keywords
Discrete time-delays; distributed time-delays; Markovian jumping parameters; mixed mode-dependent (MDD) time-delays; stochastic systems
Funding
- Engineering and Physical Sciences Research Council (EPSRC) of the U.K. [GR/S27658/01]
- Royal Society of the U.K.
- National 973 Program of China [2009CB320600]
- Alexander von Humboldt Foundation of Germany
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In this technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.
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