Observer-based sliding mode control for switched positive nonlinear systems with asynchronous switching

This paper investigates the problem of observer-based sliding mode control for switched positive nonlinear systems with asynchronous switching. The mode of controller is considered to be asynchronous with the mode of system, which means that there is a lag between the switching of controller and that of system. Firstly, an observer is designed to estimate the unmeasured states via system output. Based on the observed system states, a switched sliding mode control law and corresponding switching law based on mode-dependent average dwell time are designed to guarantee the exponential stability and positivity of the closed-loop system through the appropriate co-positive-type Lyapunov function. Then, the L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document}-gain performance of the system is analyzed. An iterative algorithm is proposed to solve the observer gain and controller gain. Finally, an application example is given to illustrate the effectiveness of the proposed method.