Robust Stability Analysis And Control Synthesis For Switched Positive Systems

Positive systems are a kind of systems whose states are always confined to the positive orthant if the initial states are nonnegative.Switched systems are a kind of systems which are composed of continuous-time or discrete-time subsystems and a rule orchestrating the switching between the subsystems.These two kinds of systems attract some scholars' attentions due to their wide application in actual life.Abundant achievements have been made in recent years.Positive switched systems are a kind of switched systems whose states are always confined to the positive orthant if the initial states are nonnegative.They are composed of continuous-time or discrete-time positive subsystems and a rule orchestrating the switching between the subsystems and have characteristics of positive systems and switched systems simultaneously.This kind of systems also has wide applications in modeling of practical systems,such as communication,aircraft,medical treatment and so on.More and more attentions have been paid to researches of positive switched systemsNowadays,there exist many results on weighted L₁-gain performance analysis and weighted L₁-gain controller design of linear positive switched systems under arbitrary and constrained switching.On the other hand,results on weighted L₁-gain performance analysis and weighted L₁-gain controller design of linear positive switched systems are relatively few.Meanwhile,due to some factors such as the change of temperature,measuring error,etc,the systems under study usually have uncertainties.The problem of obtaining the results on weighted L₁-gain performance analysis and weighted L₁-gain controller design remains to be solved.In addition,there is less study on nonlinear positive switched systems.Can the results of linear positive switched systems be extended to nonlinear positive switched systems? This is also worthy of study.Specifically,the study contents of this paper can be divided into the following sections.1.First,for a class of continuous-time positive switched linear systems which have interval uncertainties or polytopic uncertainties,based on minimum dwell time technique and time-scheduled multiple linear co-positive Lyapunov function?TSMLCLF?approach,the problems of robust stability,standard L₁-gain performance and standard L₁-gain controller design are investigated.All the results are presents in terms of linear programming,which can be solved by Matlab toolbox.2.Then,for a class of continuous-time interval positive switched nonlinear systems,based on minimum dwell time technique and time-scheduled multiple linear co-positive Lyapunov function approach,the problems of robust stability and standard L₁-gain performance are investigated.All the results are presents in terms of linear programming,which can be solved by Matlab toolbox.3.At last,for a class of discrete-time interval positive switched nonlinear systems,based on minimum dwell time technique and dwell time-dependent multiple linear copositive Lyapunov-Krasovskii function?DTMLCKF?approach,the problems of robust stability and standard L₁-gain performance are investigated.All the results are presents in terms of linear programming,which can be solved by Matlab toolbox.This thesis investigates the robust stability and L₁-gain performance of linear and nonlinear positive switched systems,and solves some problems of positive switched systems which have not been investigated yet.By constructing TSMLCLF and DTMLCKF,sufficient conditions of stability and L₁-gain performance of switched systems have been obtained,and are presnted in terms of linear programming.The effectiveness of the results is proved by numerical examples.