Stability Analysis Of The Switched Positive Systems With Unstable Mode

Since the switched positive systems own the positive constrains and switching behaviors at the same time,they have wide range of applications such as network control and mitigating viral escape.When those systems are composed of a set of unstable subsystems,it can be used to describe the dynamics of the system under certain extreme conditions.In view of this,this article takes the switched positive system composed of unstable subsystems as the research object.This thesis studies the stability of switched positive system consisting of unstable subsystems.Subsequently,this thesis also considers the distributed time-varying delay.The main researches in this thesis as followed:The globally exponentially stability of switched positive systems with unstable modes is studied.Different from the existing results,both stabilizing and destabilizing switching behaviors act in the switching sequences.Based on multiple composite copositive Lyapunov functions,some sufficient conditions about the stability are put forward to systems.Adjusting the ratio of switching behaviors can effectively compensate for state deviations caused by unstable subsystems or disturbed switching behaviors,which shows in the results.This thesis also discusses the exponentially stability of the switched positive systems when all switching behaviors are stabilizing.The simulations show the effectiveness of the results firstly.Then the relationship between the ratio of stabilizing switching behaviors and switching dwell time is discussed.Finally,the simulation verification is carried out by taking the switched positive system of the drug metabolism process as an example.The globally uniform exponentially stability of switched positive systems with distributed time-varying delay is studied,which consist of unstable subsystems.Different from the existing result,the switching behavior of this system may be stabilizing or destabilizing.Based on a multiple discretized Lyapunov–Krasovskii functional and under the premise the distributed time delay itself changes slowly and has an upper limit,the sufficient conditions for the exponentially stability of systems are proposed.On the basis of the above results,the discrete time-delay switched positive systems are considered.Time-delay-dependent stability conditions are proposed for the two case of the switching sequence in which stabilization and disturbance coexist and only the stabilizing switching behavior.The simulations show the effectiveness of the results firstly.Then the relationship between the ratio of stabilizing switching behaviors,switching parameters and time-delay parameters is discussed.Finally,simulations compared with the existing result.