Finite-Time Contractive Stability Analysis And Control Synthesis For Positive Linear Systems

Positive systems are a class of dynamic systems whose state variables are defined in the non-negative space rather than the whole linear space.It has broad application prospects in the fields of economics,ecology,and biomedical science.In recent years,the finite-time control issue draws much attentions in order to describe the transient performance of positive system in a fixed time interval.However,until now,most of the relative research focuses on the finite-time stability analysis issue and the finite-time annular domain stability analysis problem,there are few discussions about the finite-time contractive stability analysis issue of positive systems.According to this,the issues of finite-time contractive stability analysis,L₁-gain performance analysis,controller synthesis,and practical applications are investigated for several classes of positive linear systems on the basis of the existing outcomes and research methods.The main contributions are presented as follows:（1）The finite-time contractive stability analysis and control issues are investigated for general positive linear systems.First,the definition of finite-time contractive stability of positive systems is given.On this basis,with the aid of co-positive Lyapunov function method,the finite-time contractive stability criterion is established in the form of linear inequalities.Subsequently,the state feedback controllers and observer-based dynamic output feedback controller are designed,and the designed methods of corresponding controllers are also given.（2）The L₁-gain finite-time contractive boundedness analysis and controller synthesis issues are investigated for interval positive systems with disturbances.At the beginning,the definition of L₁-gain finite-time contractive boundedness is given for positive system.Moreover,the L₁-gain finite-time contractive boundedness criterion is established for interval positive linear systems through the use of the co-positive Lyapunov function method.The state feedback controller is subsequently designed to guarantee the positivity and the L₁-gain finite-time contractive boundedness of the resulting closed-loop systems.Furthermore,a convex optimization-based algorithm is presented to solve the corresponding performance index and controller parameter.（3）For impulsive positive linear systems,the finite-time contractive stability analysis and controller synthesis issues are addressed.First,the finite-time contractive stability conditions are given for positive systems under different kinds of impulsive effects are established by virtue of the co-positive Lyapunov function method and the average impulsive time interval approach.On this basis,the range of the average impulsive time interval under different cases is discussed.Furthermore,the finite-time contractive stabilization issues of positive systems under effects of“disturbance impulses”is considered,and a corresponding controller design method is given.