Reachable Set Estimation For Several Classes Of Nonlinear Time-varying Systems

Reachable set estimation plays an important role in ensuring the safe operation in practical engineering,and lots of excellent research results have been reported.However,most of the aforementioned works on the reachable set bounding have been mainly focused on linear time invariant system.It seems to us that little has been known about the explicit estimation of reachable set for nonlinear time-varying systems with time-varying delay.Therefore,we study reachable set estimation of homogeneous nonlinear time-varying systems of degree one with time-varying delay,and the reachable set estimation problem for homogeneous nonlinear time-varying systems of degree p>1 and 0<p<1.The content is arranged as follows:In Chapter 1,we briefly introduce time-varying systems and the background and significance of the research work of time-delay systems,as well as the research status and significance of the reachable set problem,and introduce the main contents of this paper.In Chapter 2,we briefly introduce the basic knowledge and notations that used in this paper.In Chapter 3,We established delay-independent criterion for reachable set estimation of homogeneous nonlinear time-varying systems of degree one.The paper will introduce a new approach which is different from the Lyapunov-Krasovskii functional method.The nonlinear term considered in this paper takes the more general form,unlike some existing works,we not need to transform the system to a time-invariant one,which leads to less conservative conditions for reachable set bounding.In Chapter 4,We established delay-dependent criterion for reachable set estimation of homogeneous nonlinear time-varying systems of degree one.Firstly,by using the Newton-Leibnitz formula,the model transformation is derived.Secondly,the research methods are improved in the existing literature.It may lead to unsolvable matrix Riccati differential equations or indefinite linear matrix inequalities.Finally,numerical examples show its validity.In Chapter 5,we discuss the reachable set estimation problem for homogeneous nonlinear time-varying systems of degree p>1 and 0<p<1.Based on the inequality method,aspecific condition was established such that the state trajectorie of the system converges asymptotically within a ball,which give a more accurate reachable set estimation.Illustrative examples are also given to show the effectiveness of the obtained results.In Chapter 6,we give the summary and prospect of the research.The main work and innovation points of this paper are briefly summarized.Some future research about this paper is also presented.