Secure stabilization of singularly perturbed switched systems under deception attacks

Deception attacks aim to destroy the integrity of data and will further lead to instability of dynamical systems. How to develop an effective analysis and synthesis approach based on system intrinsic characteristics is constantly being explored and faces great challenges. In this paper, we investigate the stabilization problem for singularly perturbed switched systems subject to unmodeled dynamics and deception attacks. Unlike most existing control schemes specialized for SPSSs, in which neither cyber attacks nor unmodeled dynamics are considered and the full system information is required, an observer equipped with a robust term is designed to estimate the system states and deception attacks bound, and an ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-dependent integral sliding mode surface is then constructed to introduce multiple time scales feature to the sliding mode dynamics. By using ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-dependent multiple Lyapunov functions and average dwell time technique, some well-conditioned stability conditions are given to ensure the stability of the state estimation error systems and the sliding mode dynamics. Moreover, an adaptive sliding mode control law is synthesized to ensure the reachability of the prescribed sliding surface, which further leads to the stability of the closed-loop system. Finally, a numerical simulation is given to show the validity of the obtained results.