Outlier-resistant state estimation for sojourn probability–based complex networks under hybrid cyber-attacks

This study focuses on the problem of outlier-resistant state estimation in complex networks subject to hybrid cyber-attacks, where sojourn probabilities and randomly varying coupling strengths are considered, in which coupling strengths are modeled by a set of mode-dependent variables. To enhance the characterization of network topology in complex networks, this paper proposes an innovative switching strategy incorporating time-varying nonhomogeneous sojourn probabilities, whose dynamic characteristics are governed by an upper-level deterministic switching signal. Subsequently, to mitigate the adverse effects of potential measurement outliers caused by abnormal disturbances or hybrid cyber-attacks on error dynamics, a state estimation scheme with adaptive saturation characteristics is proposed, whose saturation level varies adaptively in response to real-time conditions. By employing the Lyapunov stability theory combined with a mode-dependent average dwell-time approach, the stochastic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> finite-time boundedness of the resulting dynamics can be established. Finally, an illustrative example shows the advantageous properties of the designed estimation approach.