Stability Analysis For Several Kinds Of Switched Positive Systems

Switched positive systems have many practical applications in the field of en-gineering,by which,many systems,such as the intelligent formation system,the control system of traffic signal lamp,etc,can be described.Since the switched pos-itive systems inherit the features of both positive systems and switched systems,the approaches,which are employed to study the general switched systems,may give conservative results for dealing with the switched positive systems.Therefore,there exists an absolute necessity finding new and effective ways to explore the switched positive systems.The normal running of the systems start from the premise that the practical systems lies in the stability,of which analysis is the most fundamental and important problem in the control field.In this thesis,by applying dwell time approach,the stability of linear switched positive systems,the nonlinear switched positive systems,and the 2-D(two-dimensional)discrete nonlinear switched posi-tive systems are discussed in-depth based on the theoretical knowledge of Metzler matrix and nonnegative matrix.The main work and innovation points are listed as follows:1.State bounding(reachable set)estimation for linear switched positive sys-tems with mixed time-varying delays and unknown external disturbances.For the linear switched positive systems with mixed time-varying delays and unknown external disturbances,in this thesis,by making full use of the properties of Metzler matrix and non-negative matrix,the problem of system state bounding is studied by employing the mathematical induction method.In order to study the linear switched positive systems,we first consider the positive systems with mixed time-varying delays,and propose a sufficient condition for the state trajectories con-verging exponentially within a bounded domain for all non-negative initial condi-tions.Then,based on the unswitched case,which is different from the constructing Lyapunov function method,a sufficient condition for all the states within a bounded domain is given under the minimum dwell time switched signals for switched case,and the condition is simple and easy to be verified.In addition,a precise estimation of the decay rates are presented.The results show that the considered systems are globally exponentially stable when there are no external disturbance,which extend the known results.2.Stability analysis for nonlinear switched positive systems without delaysIn this thesis,we present the sufficient conditions for the stability of nonlinear switched positive systems under any degree without delays.It is known that nonlin-ear systems are different from linear case in essence.In many cases,the methods which are applicable to the linear systems are ineffective for the nonlinear systems,such as the common linear co-positive Lyapunov functions and multiple linear co-positive Lyapunov functions methods.Inspired by the approach which is used to study positive systems,we study the stability of nonlinear switched positive systems including continuous-time subsystems and discrete-time case according to construct-ing multiple max-type separate copositive Lyapunov functions,where the nonlinear functions are homogeneous functions.In detail,when 0<? ?1,we design suitable switching signals,and a sufficient condition is proposed for the exponential stability of continuous-time nonlinear switched positive systems.Moreover,we also prove the sufficient condition is necessary for the nonlinear positive systems.When ?>1,we give the asymptotic convergence criterion and exponential convergence criterion for continuous-time case and discrete-time case respectively.All the results present the precise estimation of the decay rates.3.Stability analysis for the nonlinear switched positive systems with time-varying delaysIt is well known that the time-delay systems have been extensively studied by the research community,which servers as one of the most important factors giving rise to system performance degradation.The stability of nonlinear switched positive systems under degree one with time-varying delays is considered,which includes the linear switched positive systems as a special form.Due to the coexistence of system delays and switching behavior,the jump of the systems and the effect of time delays should be considered at each switching time.The difficulties resulting from the state delays are overcome by introducing a model transformation.Then we present a sufficient condition for the global exponential stability for both continuous-time case and discrete-time case by designing appropriate switching signals.Explicit decay rates estimation are also given,which shows the influence of the system delays on the decay rates.Specifically,the larger the delay bound,the smaller the decay rate.Finally,the research results are promoted to more general delayed linear switched systems.4.Stability of the 2-D nonlinear switched positive systems with time-varying delays described by the Roesser modelThe stability of 2-D delayed nonlinear switched positive systems with time-varying delays in the Roesser model is investigated.The structure of 2-D systems is more complicated than that of the 1-D systems.In this thesis,based on the approach of dealing with the positive systems,we present a sufficient condition for global ex-ponential stability of the considered systems.The difficulties resulting from the state delays are overcome by introducing a 2-D model transformation.In addition,the in-fluence of the system delays on the decay rate is also discussed.Finally,the research results are promoted to the more general 2-D delayed linear switched systems.