Stability Analysis And Control Synthesis Of Switched Positive Systems

A switched positive system is a special kind of switched systems,which is extensively applied in diverse fields including economics,biology and transportation systems,to mention a few.It should be pointed out that the study of switched positive systems is more challenging than general switched systems due to the coexistence and interaction of the complex dynamics of switched systems and the distinct properties of positive systems.Many problems of analysis and synthesis for switched positive systems require to be solved.This dissertation is concerned with the problems of stability analysis and controller design for switched positive systems.The main contributions are as follows:The stability problems of several kinds of linear switched positive systems are addressed.The considered system consists of both stable and unstable subsystems.By limiting the number of switches and the activation time of unstable subsystems,a sufficient condition for exponential stability is established.Then,by constructing a new copositive Lyapunov function with the accumulation of time delay,the stability condition for switched positive systems with time delay is developed under the average dwell time switching.Besides,by partitioning the nonnegative state space,the state-dependent hysteresis switching law is constructed to guarantee that the switched positive system with D-perturbation and time-varying delay is asymptotically stable.The mismatched controllers are designed for switched positive systems with switching de-lay or input delay.In practice,the switching of controllers usually lags behind that of subsystems,then the asynchronous switching phenomenon is considered.By using the property of similar-ity matrix,state-feedback controllers are designed to guarantee the positivity and exponential stability of the resulting closed-loop system.Then based on the augmented state and the prop-erty of dual systems,a solvability condition of the control problem is established.Considering that not all systems' states are measurable in practice,the output feedback controller is designed to ensure that switched positive systems with time-varying delay is positive and finite-time bounded by adopting mode-dependent average dwell time approach.The stability analysis and controller design problems are studied for stochastic switched positive systems.For Markov switched positive system with homogeneous transition probability,the sufficient and necessary conditions of mean stability are presented by analyzing the time evolution of the first-order moment of system's state.Then,the mean stability criterion is derived for Markov switched positive systems with switching transition probabilities in the framework of minimum dwell time.Moreover,the problem of positive stochastic stabilization is discussed for Markov switched systems with distributed time delay and incomplete known transition rates.By constructing a new stochastic copositive Lyapunov-Krasovskii functional,a delay dependent solvability condition is established.The stability analysis and controller design problems are concerned for nonlinear switched positive system.Firstly,a class of homogeneous nonlinear switched positive system is studied.Variable cyclic dwell time switching is proposed,under which both numbers of switches and d-well time in different cycles can be variable.By using the properties of homogeneous and coop-erative vector fields,sufficient conditions for finite-time stability are derived for the case that all subsystems are finite-time stable and partial subsystems are not finite-time stable,respectively.Besides,the positive stochastic stabilization problem is studied for nonlinear Markov switched systems.For general nonlinear Markov switched systems,the parallel distributed compensator controllers are designed to guarantee that the closed-loop system is positive and stochastically stable.For nonlinear Markov switched systems with uncertainty,the uncertainty can be con-verted to the unknown element of membership degree functions.Then,a switching controller is constructed and a sufficient condition on the existence of the controller is presented in the form of linear programming.