Model Reduction For Semi-marvovian Jump Systerms

As a mathematical model describing much closer to practical engineering problems,SemiMarkov jump process has a high practical value and strong physics background.The outcome of its research closely associated with problems in control engineering, has received the attention of scholars at home and abroad, and some achievements have been successfully used in fault-tolerant control, network control system and modern communications technology, and other fields.And on the other hand,the catastrophe modeling systems usually have higher order, which brings a great deal of di?culty to the system analysis,simulation and design, so we usually hope to use low-order model to simulate high-order model within error limit. The main objective of this paper is designed for continuous-time semi-Markov jump system with model reduction, the details are as follows:First of all,the article gives the continuous-time semi-Markov jump system model and its reduced-order system model,and on this basis,determines the augmented error model.Based on the error model and the sojourn-time’s distribution probability,after choosing an appropriate Lyapunov function,we get the stability analysis condition of the model error system.And Then,based on the stability analysis condition, two methods, namely convex linearisation approach and iterative approach, were used to come up with new stability analysis conditions.Because of the existing time-varying transition rate in the stability conditions derived,we introduce lower and upper bounds of the time-varying transition rate,and by means of the sojourn-time segmentation method,we come up with a less conservative stability analysis conditions and a corresponding reduced-order solving method.At the end of the third chapter, the simulation results are given, and the effectiveness and advantages of different methods are compared and analyzed.Finally,we use some results of the third chapter to extend it to the general system,which is the model reduction problem of the semi-Markovian jump systems with time-varying delay.For the time-varying delay in the system model,by choosing an appropriate Lyapunov function and using the input-output approach,a new delay-dependent stability analysis criterion and the method of solving the reduced model are presented based on the convex linearisation approach.Note that the simulation results in the third and the fourth chapter are solved based on the LMI Toolbox.