Research On Filtering Problem For Continuous-time Switched Systems

In the recent 20 years, after the concept of hybrid dynamic systems was put forward, hybrid systems have attracted a recurring interest and attention in the control theory and engineering research community, because it exists widely in engineering and social systems. Switched systems theory developed mainly with the study of hybrid systems. Switched hybrid systems is a typical kind of complex systems in theory and engineering research, continuous-time switched systems are corresponding to the discrete-time switched systems, continuous switched systems conclude finite subsystems with continuous time dynamic, under the action of the switching signal with different mode in various time. Filtering problem is a basic research problem with wide application. The nature of filtering problem is the state estimation for input with noise measurement. Filtering is an important problem in signal and data processing. White noises are common in engineering practice. Hence in this project, we mainly study on filtering problems of several different continuous-time switched systems with white noises.This paper presents the research background and significance of the filtering problem for continuous-time switched systems, and the existing research results are analyzed in detail. Then, the main body of this article is mainly composed of three parts: the first part investigates Kalman filter designing for linear continuous-time switched systems, the discrete 5-step recursive algorithm is extended to continuous-time switched systems, after Kalman filter parameters design, giving a sufficient condition to investigate the convergence and the stability of the filtering error. Finally, a numerical simulation example is presented. The second part including parameters uncertainties, due to the limitation of Kalman filtering, parameter uncertainty leads to optimality damage, bounded variance of filtering for continuous-time switched systems with time-varying parameter uncertainty is considered. A related theorem is given to complete the analysis of filtering error dynamic system stability and find a filtering error covariance bound, numerical example is given to prove the validity of the filter design. The third part added stochastic factor, the stability of the switched stochastic systems is firstly analyzed. Then based on the stability analysis, the article gives relevant theorems of filter design to satisfy H2 performance index. Finally the filtering parameters are formulates by LMIs, and a numerical example and filtering results of the simulation are given to illustrate the correctness and effectiveness of the filtering process.Stability analysis is based on piecewise Lyapunov functions combined with average dwell time method to study the exponential stability of the system, and less conservative.