Impulsive Positive Systems Research Articles

Positive observer design for linear impulsive positive systems with interval uncertainties and time delay

This paper is concerned with the problem of positive observer design for impulsive positive systems (IPS) with interval uncertainties and time delay. A copositive Lyapunov-Krasovskii functional with exponential term is constructed. By applying the average impulsive interval method, sufficient conditions for the existence of the positive observer are established to guarantee the exponential stability of the corresponding augmented system, which ensures the designed positive observer can estimate the system states exponentially. Combined with the linear programming (LP) technique, an algorithm is developed to design the observer gain matrices. Finally, a numerical example is provided to show the effectiveness of the theoretical results.

Impulsive effects on the stability and stabilization of positive systems with delays

This study addresses the exponential stability and positive stabilization problems of impulsive positive systems (IPSs) with time delay. Specially, three types of impulses, namely, disturbance, “neutral”, and stabilizing impulses, are considered. For each type of impulsive effect, the exponential stability criterion is established utilizing the Lyapunov–Razumikhin techniques. Moreover, on the basis of the obtained stability results, the state-feedback controller design problem is investigated to positively stabilize the IPSs with time delay under different types of impulsive effects. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.

Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finite-dimensional or semi-infinite linear programs. To be applicable to uncertain systems and to control design, a lifting approach introducing a clock-variable is then considered in order to make the conditions affine in the matrices of the system. The resulting stability and stabilization conditions are stated as infinite-dimensional linear programs for which three asymptotically exact computational methods are proposed and compared with each other on numerical examples. Similar results are then obtained for linear positive switched systems by exploiting the possibility of reformulating a switched system as an impulsive system. Some existing stability conditions are retrieved and extended to stabilization using the proposed lifting approach. Several examples are finally given for illustration.

Exponential stability of impulsive positive systems with mixed time‐varying delays

This study addresses the problem of exponential stability for a class of impulsive positive systems with mixed time-varying delays. A delayed impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. By using a copositive Lyapunov–Krasovskii functional and the average impulsive interval method, a sufficient criterion of global exponential stability for delayed impulsive positive systems is established in terms of linear programming problems. A numerical example is given to show the effectiveness of the proposed method.

Stability Analysis of Impulsive Positive Systems

This paper is concerned with the problems of stability for a class of impulsive positive systems. An impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. Several sufficient criteria of global exponential stability and global asymptotical stability for impulsive positive systems are established respectively by using a linear copositive Lyapunov function. Two numerical examples are given to illustrate the effectiveness and applicability of the proposed results.