Integral sliding mode control for impulsive switched positive nonlinear systems under asynchronous switching

This paper addresses the integral sliding mode control (ISMC) problem of impulsive switched positive nonlinear systems under asynchronous switching. An ISMC method based on a new switched integral sliding function and time-varying switching gains is proposed, which allows the controller switching to lag behind the subsystem switching. The new sliding function is constructed as a switching function related to the switching mode, while the switching gains are devised as piecewise functions based on a partition strategy on the dwell intervals. The proposed ISMC law consists of a nonlinear discontinuous part and a linear control part, in which the nonlinear discontinuous part ensures the integral sliding surface to be continuous and to be reached from the beginning, and the linear part is responsible for positivity, stability and \(L_1\) $L_1$ -performance. By using a co-positive piecewise time-varying Lyapunov function, criteria for designing the desired switching gains are derived in a convex optimization framework. Finally, a numerical example is provided to illustrate the effectiveness of the proposed ISMC method.