Stability Analysis,L₁ Gains And H_? Feedback Control Of Switched Positive Systems

Many systems in life are positive systems,Because its physical limit cannot switch too fast,dwell time needs to be introduced.The theory of switching systems is directly applied to switching positive systems which may not be true due to the positive system is nonnegative,so it becomes a hot topic to study the properties of switched positive systems under dwell-time constraintThe common Lyapunov function is usually used to study the stability of the system,but there are limitations to share a linear co-positive Lyapunov function among multiple subsystems for discrete time switched linear positive systems under dwell-time constraint.In this paper,a time-varying piecewise linear copositive Lyapunov function method is proposed,and a sufficient condition is established to ensure the asymptotic stability of the system.Dwell time which makes the system asymptotically stable is smaller compared with the common linear co-positive Lyapunov functionIn addition,the method is used to analysis L1 gain of discrete time switched linear positive systems,a sufficient condition ensuring the unweighted ?-L1 gain of the system is derived,the relationship between the dwell time and ?-L1 gain is derivedFurther,the time-varying H? feedback synchronous controller and asynchronous controller are designed for the system,which keeps the closed-loop system positive and having a minimum?-L1 gain,it is concluded that synchronous control is more effective than asynchronous control in suppressing disturbance input impact on the performance of system,which makes the gain drop lower.the smaller the lag time is,the lower the gain will be under the same dwell time in the asynchronous control.Finally,the corresponding numerical simulation in each part is given to demonstrate the conclusion.