Study On Dissipativity And Output Regulation Problem Of Switched Positive Linear Systems

A switched positive system,consisting of positive subsystems,is a special kind of switched system.Such a system is of great significance both in theory development and engineering applications.Positivity is the unique property of positive systems and a natural attribute of many practical systems.In recent years,the study of switched positive systems has received considerable attentions in the field of control.However,the dynamic behavior and the research of switched positive systems become more complicated and difficult,due to the coexistence and interaction between the switching behavior and the positivity of systems.Due to the lack of effective tools and methods,at present,the research of switched positive systems is still in its infancy.On the other hand,dissipativity is a very useful system property which offers an effective tool for the analysis and design of control systems and a systematical theory has been formed.For switched positive systems,dissipativity possesses novel characteristic,which exploits linear supply rate and linear storage function to depict dissipativity.But,the results on such issue are still limited up to now,and there are many analysis and design problems deserving to be solved.This dissertation investigates the problems of dissipativity and output regulation for switched positive linear systems.The main results of this thesis are five aspects.(1)The dissipativity and related properties of switched positive linear systems are investigated.First,multiple linear co-positive storage functions and multiple linear supply rates are employed to describe dissipativity of the systems.Then,a novel concept of dissipativity is presented,which depicts the overall dissipativity property of positive switched systems without the requirement of the classic dissipativity property of each positive subsystem.Second,by partitioning the nonnegative state space,we devise a switching strategy,which relaxes the the requirement of the continuity of linear co-positive storage functions for two adjacent subsystems on the switching instants,and allows even a certain amount of increase.Further,by employing dissipativity,we design certain specific forms of feedback laws to achieve asymptotic stability with the aid of detectability of subsystems.Finally,dissipativity and positivity are shown to be preserved under the positive feedback interconnection.Sufficient conditions are given in form of linear vector inequality,which can be solved by means of linear programming tool.(2)The problem of feedback dissipativity is investigated by using the multiple linear co-positive storage functions method for switched positive linear systems in both continuous-and discrete-time domains.When all subsystems are nondissipative,we devise a state-dependent switching law such that the switched positive linear systems have dissipativity.When dissipativity cannot be achieved by the design of a switching law alone,we show how to perform the co-design of state-feedback controllers for individual subsystems and a state-dependent switching law to achieve positivity and dissipativity of the closed-loop system.Finally,the dissipativity-based stabilization problem is researched and sufficient conditions ensuring asymptotic stability the considered systems are attained.(3)The issue of stability with guaranteed cost for switched positive linear systems are studied by constructing a novel linear co-positive Lyapunov function.Two different switching policies are devised.The first one relies on continuous-time strategy and the other depends on the sampled-data strategy.The designed switching policies not only render the considered systems globally exponentially stable with a pre-specified adequate level of performance,but also decreases the switching frequency to rule out the Zeno behavior.Moreover,the solvability condition is established.(4)Based on the multiple linear co-positive Lyapunov functions method,the solvability of the classical output regulation problem is discussed.When the system state together with the external input are available,sufficient conditions ensuring the solvability of the problem as well as positivity are given using the dual design of full information feedback controllers for subsystems and a state-dependent switching law.Besides,when only the output tracking error is available,a switching rule depending on the output tracking error is designed which,together with the dynamical error feedback controllers,guarantees the positivity of the studied systems and the solvability of the problem.(5)We consider an unmodeled external disturbance affecting the systems and the exogenous systems.The almost output regulation problem for switched positive linear systems is studied under the framework of different coordinates transformations for subsystems.This study is composed of two parts as follows:(i)Based on the average dwell time method,sufficient conditions for the problem to be solvable and positivity are obtained by exploiting state feedback controllers and error feedback controllers,respectively,where the solvability of the problem for each subsystem is assumed.(?)When the problem for each subsystem may not be solvable,the state feedback controller and a novel state-dependent switching rule satisfying a dwell time constraint is jointly devised to cope with the problem.Additionally,the use of different coordinates transformations for subsystems can reduce the conservativeness than the adoption of common one.Finally,the conclusions and perspectives are presented.