Analysis And Synthesis Of Switched Positive Systems With Dwell Time Constraints

Switched positive systems are a kind of systems which are composed of several continuous-or discrete-time subsystems and a rule orchestrating the switching between the subsystems.They have the property of both positive systems and switching systems.Switched positive systems are increasingly concerned by scholars because of their wide application in actual life.Switched positive systems are more complex than positive systems and switched systems because of their more complex forms and more change-able properties.Compared with the positive systems and switched systems,the research results on switched positive systems are relatively less.The research on the analysis and synthesis of switched positive systems with dwell time constraints needs to be fur-ther enriched.Hence the research on switched positive systems has important theoret-ical and practical significance.In this dissertation,based on the basic theories of ma-trix theory,switched system theory,positive system theory,by using the minimum dwell time method,average dwell time method,timer-dependent multiple linear copositive Lya-punov function method,discretization method,sum of square approximation method and other research methods,switched positive systems with dwell time switching signals are studied from the perspectives of stability and stabilization,asynchronous L₁-gain control,state observation,asynchronous L₁-gain filtering and so on.Specifically,the research work and innovation of this thesis are as follows:1.The stability and stabilization problems are studied for switched positive lin-ear systems(SPLSs)with minimum dwell time.Firstly,the stability and stabilization problems are studied for the continue-time case,several stability and stabilization con-ditions are presented in terms of linear programming which contain infinite-dimensional terms,and the relation between these conditions is illustrated.These conditions which contain infinite-dimensional terms can be transformed into computable ones by using a discretized approach.The simulation results show that compared with the literature,less conservative results can be achieved with the help of an algorithm designed by us.Then,some novel stability and stabilization conditions are presented for the discrete-time case with dwell time,and the relation between these conditions is also illustrated.These ob-tained conditions for discrete-time systems are given in terms of finite-dimensional linear programming,which can be solved directly.2.The asynchronous L₁-gain controller design problems are studied for SPLSs.Firstly,the L₁-gain performance analysis and asynchronous L₁-gain controller design problems are studied for continue-time SPLSs with interval and polytopic uncertain-ties.Then,the L₁-gain performance analysis and asynchronous L₁-gain controller design problems are studied for discrete-time SPLSs with polytopic uncertainties.By utilizing a timer-dependent multiple linear co-positive Lyapunov function approach,sufficient con-ditions on L₁-gain performance are presented for both continue-and discrete-time SPLSs.Next,based on the L₁-gain performance analysis results,asynchronous controller design schemes are presented for both continue-and discrete-time cases.The simulation re-sults show that the designed asynchronous L₁-gain controller can ensure the closed-loop system's positivity,stability and non-weighted L₁-gain performance.3.The stability and observer design issues are addressed for continue-time SPLSs with average dwell time.Firstly,by using a reverse-timer-dependent linear co-positive Lyapunov function approach,a novel stability criteria is derived for continue-time SPLSs with average dwell time.Then,based on the stability criteria,an observer design scheme is presented such that the unknown states of the systems can be tracked asymptotically.The observer gains can be obtained directly by solving a set of sum of square program.The simulation results show that compared to the traditional multiple linear co-positive Lyapunov function approach,less conservative conditions can be obtained by the reverse-timer-dependent multiple linear co-positive Lyapunov function approach.4.The asynchronous L₁filtering problem is studied for continuous-time SPLSs with dwell time.Firstly,By using a timer-dependent multiple linear co-positive Lyapunov function approach,a novel sufficient condition characterizing a non-weighted L₁-gain performance of the augmented systems is established.Then,with the help of the L₁analysis results,a novel asynchronous filter design scheme is presented such that the augmented systems based on original systems and filtering error systems are stable and have a prescribed non-weighted L₁performance.The filter gains can be obtained directly by solving a set of linear programming.The simulation results show that a smaller L₁-gain index can be achieved by the novel filter design scheme compared with the traditional ones.