Robust Stability And Stabilization For Switched Positive Systems With Time Delays

Switched systems have received the attention of the majority of scholars,owing to the significance in theory and application.The positive system can be referred to as a type of dynamic system whose state is subject to non-negative constraints,and its state trajectory is limited to non-negative sub-regions.The switched positive system that can be applied in many fields is a kind of switched system whose subsystems are all positive systems.For instance,TCP protocol applied in communication network system,formation flight control system,virus spreading control system.In addition,time-delays that have a great impact on the stability and accuracy of the system are very common in various practical engineering systems.In this thesis,we focus on the stability analysis and stabilization design of switched positive systems.The main work is as follows:Firstly,we focus on the study of the state-bounding observer problem for continuous and discrete interval positive system with time delays under the L1(l1)-induced performance.The main idea is as follows.A pair of upper bounding and lower bounding observers are proposed to estimate the state of positive system.Under the estimation of the upper and lower bounds,the state estimation is always limited to the bounded range and satisfies the L1(l1)-induced performance.Sufficient conditions are presented to design of state-bounding observer.In fact,the stability and state positivity requirements cannot be met at the same time in the augmented system,the state estimation feedback controller cannot be designed to stabilize the system?Therefore,we design a switching state feedback controller.On the basis of the positivity of the augmented system,we prefer the switching law of the state-dependent to stabilize the augmented system whose subsystems may be unstable.Secondly,we focus on the study of the stability of continuous switched positive system with time delays whose all subsystems are unstable.The main idea is to compensate for the divergence of the state caused by the unstable subsystem by designing a suitable switching mechanism,so that the switched positive system with time-delays is asymptotically stable.By the model-dependent dwell time method and a class of discretized co-positive LyapunovKrasovskii functional,the sufficient conditions for the stability of the positive switched system with time-delay are obtained if all the subsystems are unstable.By applying the above method to the interval switched positive system with time delays,the robust stability problem can be solved.Finally,the stability analysis of discrete-time systems with time-delay under arbitrary switching signal is studied.For the controlled system,the original system with varying timedelays is converted into an equivalent input-output system with constant time-delay by model transformation and the small-gain theorem.The stability of the interconnection system is studied by the co-positive Lyapunov-Krasovskii functional and scaled small-gain theorem.In addition,the common state feedback controller is designed to stabilize the system.The effectiveness and feasibility of the results are illustrated by simulation.