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...the switching signal where s(x) = 0 is called the switching surface. For certain system parameters and selection of s(x) it can be shown that Eq. 1 exhibits a form of behavior known as a sliding mode =-=[1, 6]-=-. Here, the trajectory of x is attracted and subsequently confined to the n-dimensional surface s(x) = 0, which in the case of a sliding mode is also termed the sliding surface. The necessary and suff...

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...cture Systems and the Sliding Mode Variable structure systems are a class of hybrid dynamical systems that consist of a family of subsystems and one or more rules that govern the switching among them =-=[6]-=-. Such systems exhibit both continuous and discrete states of behavior important for modeling some underlying characteristics of cyber-physical systems. For example, the switching behavior represents ...

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...en as the stable focus of A2 given by (1.1198, 0). If s > 0, the system dynamics switch to system A1; otherwise, the system dynamics switch to system A2. Due to the chattering effects, as detailed in =-=[3]-=- we employ a hysteresis effect to make the switching frequency finite. We assume that an attacker applies a switching attack from 0 to 2.5 seconds employing the unstable sliding mode s = δ1 + 0.5ω1, w...

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...functions s(x) and problem dimensionality. However, assuming linear models of dynamics and the switching surface and for a single switch case, the following theorem has been derived by the authors in =-=[4]-=- regarding the existence of such sliding modes. Theorem 1 (Existence of a Sliding Mode). Given the variable structure system: ẋ = { A1x+ b1, s(x) > 0 A2x+ b2, s(x) ≤ 0 (6) where x ∈ Rn×1, Ai ∈ Rn×n, ...

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...ching attacks in which an opponent can employ local state information to design a switching sequence that can destabilize synchronous generators leading to various forms of instability and power loss =-=[2, 3]-=-. In this work, we extend our research to demonstrate an approach to mitigation within this variable structure system framework. Specifically, we study strategies employed by a power system operator i...