Network-based stability analysis and synthesis for stochastic system with Markovian switching

Abstract

This thesis is concerned with the network-based stability analysis and synthesis of stochastic systems with Markovian characteristics. Two difficulties raised in Networked Control Systems (NCSs) are considered: Random Network Communication Delay and Quantization (state quantization and input quantization are discussed respectively). Four types of research problems are investigated. They are: 1. Stabilization of Markovian jump linear system over networks with random communication delay. 2. Logarithmic Quantizer design for Markovian jump linear system via Input Partition method and via State Partition Method. 3. Quantization error estimation and observer-based controller design. 4. Robust quantized filtering for Ito stochastic system with Markvian switching. It is well known that, the network communication transmission delay is a common phenomenon in NCSs. In Problem 1, the main work is concerned with the stabilization problem for a networked control system with Markovian characterization in the existence of random communication delay. We consider the case that the random communication delays exist both in the system state and in the mode signal which are modelled as a Markovian chain. The resulting closed-loop system is modelled as a Markovian jump linear system with two jumping parameters, and a necessary and sufficient condition on the existence of stabilizing controllers is established. The state/input quantization is another important phenomenon in NCSs. In Problem 2, the input quantization is addressed. We shall first deal with the problem by designing a quantized control strategy for a class of discrete time Markovian jump linear systems using input partition method. We generalize the classic static quantizer design method to Markovian jump linear system. The concept of mode-dependent logarithmic quantizer is presented, which is employed to ensure the stochastic stability of the quantized closed-loop system. Secondly, in Problem 2, we aim to design another quantized control strategy for discrete time Markovian jump linear systems via state partition method. We introduce the concept of stochastically quadratically stabilizing a mode-dependent quantizer associated with a series of new definitions. The proposed mode-dependent quantizer can stabilize the quantized closed-loop system and overcome the effect of Markovian switching on system stability. In Problem 3, we shall discuss the problem of state quantization. Most of the quantized control schemes in existing literature are focused on the controller/filter design using the quantized state/output signal. Since error always exists between the quantized signal and the original one, the designed controller/filter in the framework of traditional quantized control scheme may not achieve an ideal performance. Hence, we consider a quantized control strategy by decoupling the original state/output from the quantized signal by using the observer technique. A quantization-tolerant controller is then designed to stabilize the closed-loop quantized system. We shall employ this control strategy to deal with the stabilization of continuous linear systems with limited communication capacity. In Problem 4, we investigate a filtering design for uncertain stochastic systems with saturating quantized measurements. There are time-varying parameter uncertainties, and state and external-disturbance-dependent noise in the plant. In the presence of output quantization, we consider the design of robust quantized filters for Ito stochastic systems, and sufficient conditions are obtained such that the filtering error systems are robustly exponentially stable.

Date of Award	2 Oct 2009
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Wing Cheong Daniel HO (Supervisor)