Stability Analysis And Control Synthesis Of Switched Positive Systems

Positive systems are a kind of dynamic systems whose states are always nonnegative whenever the initial conditions are nonnegative.Switching systems are a class of hybrid systems,which consist of a family of subsystems and a rule orchestrating the switching between them.Switched positive systems are a kind of switched systems whose states are always restricted to the positive orthant.They contain characteristics of positive systems and switched systems contemporaneously.This kind of systems also has extensive applications in modeling of practical systems,such as medical science,communication,biology and so on.More and more attentions have been paid to researches of switched positive systems.Compared with the positive systems and switched systems,the research results on switched positive systems are relatively less.Hence,it is of theoretical significance and practical value to analyse the problems related to the switched positive systems.In this thesis,we focus on the stability problem and controller design for several classes of switched positive systems.The main work of this dissertation consists of the following aspects:The problem of stability analysis,-gain characterization and state feedback controller design for uncertain Markovian hybrid switched positive systems is investigated.The key feature is that the switching mechanism is described by a general class of hybrid switching laws,which is comprised of Markovian switchings and deterministic switchings.By using the mode-dependent time interval segmentation technique,multiple time-varying copositive Lyapunov functions are constructed.Then,the criteria ensuring the stochastically exponential stability and -gain are derived.Based on the obtained results,the statefeedback controller design problem is studied.Finally,a numerical example and a practical one are provided to illustrate the effectiveness of the obtained results.The problem of the stability for impulsive switched positive systems with time-varying delays is studied.The obvious distinctions between the previous results and ours are that the impulses are not synchronous with the switchings.Specifically,a general class of hybrid switching laws,including both Markovian switchings and dwell time switchings,describe the switching signals,and the impulsive signal is described by means of average impulsive interval method.In order to better reflect the reality,both state delay and impulsive delay are taken into consideration.By using the multiple time-varying copositive LyapunovKrasovskii functionals,sufficient conditions to ensure the stochastically exponential stability of impulsive switched positive systems with time-varying delays are obtained.Lastly,the theoretical findings are substantiated with illustrative example.The problem of the stability analysis for positive systems with multiple delayed impulses is addressed.Two different methods are used to describe the time delay term.One is the mode-dependent average impulsive delay method and the other is the Markov chain method.At the same time,two types of impulsive(i.e.,disturbance impulses and stabilizing delayed impulses)are considered.Moreover,sufficient conditions of mean stability are derived by utilizing the Lyapunov stability theory.Finally,illustrative examples are presented to show the validity of the obtained results.