Quantized Feedback Control For Markov Jump Systems

Network control systems (NCS) is becoming the major trend of control theory,not only in theoretical exploration but also in industrial area. The emerging researchhas been addressed on quantization, as a major mechanism, which introduced for thelimited bandwidth due to the information flow. Moreover, motivated by the powerfulmodeling capability of Markov chains, the packet loss among NCSs can be modeledas the Markov jump system in specific jump scheme. So what we concern are thestability and performance of quantized feedback control of Markov jump system, themain contribution of this paper are as follows:In the first part, we investigate the quantized state feedback control for Markovjump linear systems subject to incomplete transition probabilities. A criterion is pro-posed to ensure mean square stabilization of the closed-loop system, where the efectof current mode observation logarithmic quantizer is counted for. Furthermore, a con-straint in linear inequality matrix form proposed on the H∞control problem to quantizedMarkov jump linear systems.Second, for the static quantized output feedback control, we investigate the situ-ations both on incomplete transition probabilities and normal condition. Two criteriawith a equation constraint are proposed to ensure stochastic stabilization of the closed-loop system, which can obtain the quantized output controller with coarsest density.The extended H∞control problem of Markov jump linear systems is also significant.By comparing these two diferent situations, we discuss the impact of the amount ofinformation on the density of quantization.Third, concerning with the problem of observer-based output feedback control forMarkov jump systems with quantized input, a new sufcient condition is established toguarantee the stochastic stability of the closed-loop system, and implement the decou-pling design of observer and controller.Some numerical simulations demonstrate the efectiveness of above proposed meth-ods.