Dwell-time-based Stability, Stabilization And L₁-gain Property Of Switched Positive Systems

Switched systems are widely used in aerospace,computer networks,chemical produc-tion and many other fields.On the other hand,switched positive systems are a special type of switched systems,which have been found in many practical applications such as economics,biology,transportation systems and so on.For the study of switched positive systems,we not only take into account the complex dynamic behavior of switched systems,but also ensure the positive nature of positive systems,which makes the stability analysis and the stabilization design of switched positive systems extremely difficult.Therefore,the analysis and control of switched positive systems are important to scientific practical application,which has become an important problem in recent years.Therefore,this thesis mainly studies the stability,stabilization and L₁-gain property of switched positive systems.The main contents obtained in this thesis are as follows:In Chapter 1,we present a survey.Firstly,a brief overview of switched systems is given.Secondly,the research significance,the research methods and the-state-of-the-art of switched positive systems are summarized.Then,the main works and the structure of this thesis are briefly introduced.In Chapter 2,we study the exponential stabilization of switched positive systems based on the dwell time switching signal.In the references,the results on stability anal-ysis of switched positive systems are obtained under the assumption that there exists at least one stable subsystem.However,in this Chapter,we assume that all subsystems are unstable.By constructing a class of multi-time-varying linear copositive Lyapunov functions,a sufficient condition for exponential stabilization of switched positive systems is obtained by constraining the upper and lower bounds of the dwell time,restricting the growth rate of the subsystem’s“energy”,and reducing the“energy”of adjacent switching points.The feasible solution of the sufficient condition can be solved by linear program-ming.When all subsystems are stable,the constraint of upper bound of the dwell time can be removed,that is,when the dwell time has only the lower bound,and a sufficient condition for exponential stabilization of switched positive systems is given.Finally,the effectiveness of the proposed methods is verified by simulation examples.In Chapter 3,we investigate the exponential stabilization of a class of switched posi-tive systems by co-designing dwell time switching signal and controller of each subsystem.Based on the results of Chapter 2,we study the exponential stabilization of switched positive systems with control inputs.Firstly,under the assumption that all subsystems can not be stabilized,by constructing a class of multi-time-varying linear copositive Lya-punov functions,we obtain a sufficient condition for exponential stabilization of switched positive systems by co-designing the state feedback controller of the subsystem and the corresponding dwell time switching signal.The feasible solution of the obtained suffi-cient condition can be solved by linear programming.Secondly,under the assumption that all subsystems can not be stabilized,by constructing a class of multi-time-varying linear copositive Lyapunov functions,we obtain the sufficient condition for exponential stabilization of switched positive systems by co-designing the output feedback controller of the subsystem and the corresponding dwell time switching signal.Finally,an example is provided to demonstrate the effectiveness of the proposed method.In Chapter 4,we investigate the L₁-gain property of a class of switched positive systems without internal stable subsystems based on dwell time switching signal.Based on the results in Chapter 2,we further study the L₁-gain property of a class of switched positive systems with external disturbance input.Under the assumption that there is no internal stable subsystems,by constructing a class of multi-time-varying linear coposi-tive Lyapunov functions,the sufficient condition for L₁-gain with exponentially stable of switched positive systems is proposed by restricting the upper and lower bounds of dwell time.Finally,an example is provided to demonstrate the effectiveness of the proposed method.In Chapter 5,we investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching,whose nonlin-ear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler.Firstly,for the case of nonlinear programming,we construct a class of multi-time-varying nonlinear copositive Lyapunov functions obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.Secondly,for the case of linear programming,we relax the constraints of the Lyapunov function“energy”strictly decreasing over the entire interval and require only the strict decrement of the“energy”of the designed Lyapunov function at the adja-cent switching points.Then,the sufficient conditions on the exponential stability of the switched systems are obtained in terms of linear programming.Finally,the effectiveness of the two methods is verified by simulation examples.The conclusions and perspectives end the dissertation.