Robust Stability Analysis Of Uncertain Sampling System

The coexistence between continuous-time systems signals and discrete-time systems signals is realized by sampled-data systems. With the development of digital control systems and networked control systems, the study of sampled-data systems attracts more attention. The stability of sampled-data systems is the precondition of their normal work, and the computational burden and the data transmission rate of sampled-data systems can be decreased with the increase of the sampling intervals, so it is significant in theory and application to study the stability of the sampleddata systems. As uncertainties appear in the practical engineering, the study of the robust stability for sampled-data systems with polytopic uncertainties is also full of scientific research value.The problem of robust stability for sampled-data systems with polytopic uncertainties is studied in this paper. At first, a new Lyapunov functional is constructed. The asymptotical stability criteria for sampled-data systems are derived based on the Lyapunov stability theory. Then, the stability criteria are extended to sample-data systems with polytopic uncertainties and a robustly asymptotical stability criterion is derived. The stability criteria obtained in this paper can be proved by the Matlab LMI toolbox.In the first chapter, the study background and the significance of sampled-data systems are analyzed, and then the present study situation of the stability for sample-data systems is introduced.At last, the problems to solve are given.In the second chapter, the Lyapunov stability theory, LMI methods and some significant lemmas are introduced simply.In the third chapter, the stability for certain sampled-data systems is discussed. An improved Lyapunov functional is obtained by introducing the integral of state and the cross terms of the integral and sampling states. Stability criteria with less conservatism are obtained by using this Lyapunov functional and the improved Jensen inequality reported recently. Then, the stability criteria are extended to sampled-data systems with polytopic uncertainties. At last, simulation results show the stability criteria proposed in this paper are less conservative than those from some existing literatures.In the fourth chapter, the stability criteria in the third chapter are further improved. The sampling state in the right end of the sampling interval is also introduced into the Lyapunov functional,which improves the Lyapunov functional in the third chapter. This Lyapunov functional is only required to be positive definite at the sampling instants and may be not continuous at the sampling instants. The results in the third chapter are further improved. Then, the improved stability criteria and the robust stability criteria are obtained. At last, some examples are used to show the stability criteria in this chapter have less conservatism than those in the third chapter.In the fifth chapter, the content of this paper is concluded and the conservatism of proposed stability criteria in this paper is analyzed. Then, the outlook of the future work is introduced.