Proportional–Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks

This article investigates the asynchronous proportional–integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

I. Introduction

Due to the distinct application ability, complex networks have been extensively concerned over the past decades, for instance, traffic networks and grid networks [1]–[5]. Complex networks are a large-scale dynamic, which composes of certain network topology and interconnected nodes, each of which signifies a type of nonlinear dynamical. Consequently, much valuable research effort has been applied to complex networks due to their structural complexity, including synchronization, quasi-synchronization, and so on [6]–[8].