Dual-channel adaptive event-triggered <i>H</i> _∞ / <i>L</i> ₂ − <i>L</i> _∞ secure control for impulsive switched systems subject to unstabilizable subsystems and hybrid attacks

Designing secure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> control for impulsive switched systems with unstabilizable modes in the context of cyber attacks poses a complex challenge. Current event-triggered control approaches are often ineffective in simultaneously addressing unstabilizable modes, countering cyber attacks, and enhancing communication efficiency. In order to tackle these challenges, this study investigates the dual-channel adaptive event-triggered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> secure control issue for nonlinear impulsive switched systems characterized by unstabilizable modes. A corresponding neural network (NN)-based switched observer contingent on whether the Denial-of-Service (DoS) attack is active or inactive is designed to estimate the unmeasurable state of the original system. The dynamics of the concerned switched system combined with dual-channel adaptive event-triggered mechanism (DC-AETM), observer and hybrid attacks are formulated as a new compound switched system. Then, novel sufficient conditions are established by employing the compound switched signal, the average dwell time (ADT) method, and Lyapunov stability theory. These conditions guarantee that the closed-loop system attains mean-square exponential stability while preserving the mixed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> performance index. The findings demonstrate the compromise between the ADT ratio of stabilizable modes, unstabilizable modes, the compound switched signal, and the system’s resilience to hybrid attacks. Moreover, a co-design method of DC-AETM parameters and observer-based controller gain matrix is proposed. Compared with some existent results, our results have improved in three aspects: (1) the innovative DC-AETM eliminates the Zeno phenomenon naturally and additionally conserves resources; (2) the restrictions on DoS attack signals and switched signals are relaxed by employing ADT method; (3) the mixed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> / <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> secure control challenge for impulsive switched systems with unstabilizable modes is first solved. Ultimately, the practical applicability of the obtained results is highlighted through the examples of switched circuit systems and single-link robot arms.