Finite-time H∞ synchronization control for nonlinear time-varying systems through the state-dependent switching PI controller and interval matrix method

H. Zeng

doi:10.1016/j.jfranklin.2025.108257

Finite-time H∞ synchronization control for nonlinear time-varying systems through the state-dependent switching PI controller and interval matrix method

2025-11-20

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Nallappan Gunasekaran

DOI：10.1016/j.jfranklin.2025.108257

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This paper investigates the finite-time H∞ synchronization (H∞ FTS) problem for nonlinear time-varying systems (NTVSs) subject to time-varying delays and external disturbances. The interval matrix method (IMM) is introduced, and its definitions, properties, and geometric interpretations are established to address the challenges induced by time-varying coefficients. Based on this framework, sufficient H∞ FTS conditions are derived in the form of solvable linear matrix inequalities (LMIs). A novel control strategy is proposed, where the online state-dependent switching PI controllers (SDSPICs) are designed and tuned using a global search algorithm (GSA)-based optimization scheme. This strategy switches between proportional–integral and proportional modes to enhance convergence performance while reducing control energy cost. Simulation results validate the theoretical analysis and demonstrate the superior performance of the proposed SDSPIC compared with the traditional PI controller.

Finite-time H∞ synchronization control for nonlinear time-varying systems through the state-dependent switching PI controller and interval matrix method

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