Synthesis of Dynamic Systems with Markovian Characteristics

This dissertation, "Synthesis of Dynamic Systems With Markovian Characteristics" by Junlin, Xiong, 熊軍林, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled Synthesis of Dynamic Systems with Markovian Characteristics submitted by Junlin Xiong for the degree of Doctor of Philosophy at The University of Hong Kong in August 2007 The thesis is concerned with the synthesis of dynamic systems with Markovian characteristics. Two classes of systems are considered: Markovian jump linear systems and networked control systems. Three types of problems are investigated. They are (a) robust stabilization, robust H control, robust H control and robust H filter design of 2 1 1 uncertain Markovian jump linear systems; (b) stabilization of Markovian jump linear systems with delayed system information; and (c) stabilization of networked control systems with bounded time delay and packet loss. For problem (a), the system under consideration is a continuous-time Markovian jump linear system. The uncertainties are norm bounded in the system matrices and element-wise bounded in the mode transition rate matrix. An improved model of the mode transition rate uncertainties is described, which enables the use of the probability constraints on the rows of the mode transition rate matrix to reduce the conservatism of the results. Sucient conditions are given for the designs of the robust stabilizing controllers, robust H controllers, robust H controllers and fixed-order robust H 2 1 1filters. For problem (b), the system under consideration is a discrete-time Markovian jump linear system. Both the system state and the system mode are time delayed. The delay in the system state is time-varying and bounded, while that in the system mode is constant. The delay in the latter case manifests as a constant mismatch of the modes between the system and the controller. The resulting closed-loop system is shown to be a time-varying delayed Markovian jump linear system with extended operation modes. A sucient condition is provided for the design of the controller with the delayed information. For problem (c), two techniques are developed for the stabilization of networked control systems. One is to use packet-loss dependent Lyapunov functions. In this case, the process to be controlled is a linear discrete-time system. The communication net- work has the bounded packet-loss behavior characterized either by an arbitrary process or by a Markovian chain. The stabilization problem is tackled. The other technique is to employ a special zero-order hold. In this case, the zero-order hold has a logic to apply the newest control input data to control the process. Under this framework, the networked control system with both time delay and packet loss is discretized to a discrete-time system with input delay. Several sucient conditions are given for the design of the networked controllers. All the obtained conditions are given in terms of either linear matrix inequalities only or linear matrix inequalities with equality constraints. Numerical examples and simulations are used to demonstrate that (a) it is necessary to consider the uncertainties in the mode transition rate matrix; (b) the results developed in the thesis are more powerful than existing ones; (c) the delay in the system mode is critical for the control of Markovian jump linear systems with delayed information; and (d) the networked controllers can be eectively designed by the developed theories. DOI: 10.5353/th_b3897933 Subjects: Markov processes Control theory