Hybrid Impulsive Control of Stochastic Systems with Multiplicative Noise Under Markovian Switching |
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| Authors: | S. Sathananthan N. Jameson I. Lyatuu L. H. Keel |
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| Affiliation: | 1. Department of Mathematics and Center of Excellence in ISEM , Tennessee State University , Nashville , Tennessee , USA satha@coe.tsuniv.edu;3. Department of Mathematics and Center of Excellence in ISEM , Tennessee State University , Nashville , Tennessee , USA;4. Department of Electrical and Computer Engineering and Center of Excellence in ISEM , Tennessee State University , Nashville , Tennessee , USA |
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| Abstract: | A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results. |
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| Keywords: | Impulsive systems LMIs Stochastic stability Stochastic systems |
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