Quantized stabilization of stochastic systems with multiplicative noise under Markovian switching |
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Authors: | S. Sathananthan Mohammad Habibi Netra Dahal |
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Affiliation: | 1. Department of Mathematics and Center of Excellence in Information Systems, Tennessee State University, Nashville, TN, USA;2. Department of Mechanical Engineering, Tennessee State University, Nashville, TN, USA;3. Department of Electrical and Computer Engineering and Center of Excellence in Information Systems, Tennessee State University, Nashville, TN, USA |
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Abstract: | A problem of quantized state feedback quadratic mean-square stabilization of discrete-time stochastic processes under Markovian switching and multiplicative noise is considered. A static quantizer is used in the feedback channel and the jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. It is shown that the coarsest quantization density that permits quadratic mean-square stabilization of this system is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special linear stochastic Markovian switching control system. Also, sufficient conditions for exponential mean-square stabilization of such systems are also explored. An example is given to demonstrate the obtained results. |
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Keywords: | Logarithmic quantization stochastic systems Markovian switching systems discrete- time systems |
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