<p>This paper addresses the problem of decentralized finite-time guaranteed cost control for a class of nonlinear interconnected fractional-order systems subject to parameter uncertainties and external disturbances. A novel integral quadratic performance index is introduced to evaluate the system behavior over a finite time interval, reflecting both stability and performance objectives. By employing tools from fractional-order calculus, finite-time stability theory, and advanced inequality techniques, a new set of sufficient conditions is derived to ensure that the closed-loop system is robustly finite-time bounded while guaranteeing an upper bound on the cost function. The proposed control framework includes both state-feedback and output-feedback strategies, formulated in terms of tractable strict linear matrix inequalities, which are amenable to efficient numerical implementation via standard Linear Matrix Inequality solvers. The theoretical results not only generalize existing approaches to integer-order systems but also fill a gap in the literature concerning fractional-order large-scale nonlinear systems. Two illustrative numerical examples are presented to validate the proposed methodologies, demonstrating the effectiveness and robustness of the control schemes under various uncertainties and nonlinearities.</p>

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Decentralized finite-time guaranteed cost control for a class of interconnected nonlinear fractional-order systems

  • Nguyen Thi Phuong,
  • Mai Viet Thuan

摘要

This paper addresses the problem of decentralized finite-time guaranteed cost control for a class of nonlinear interconnected fractional-order systems subject to parameter uncertainties and external disturbances. A novel integral quadratic performance index is introduced to evaluate the system behavior over a finite time interval, reflecting both stability and performance objectives. By employing tools from fractional-order calculus, finite-time stability theory, and advanced inequality techniques, a new set of sufficient conditions is derived to ensure that the closed-loop system is robustly finite-time bounded while guaranteeing an upper bound on the cost function. The proposed control framework includes both state-feedback and output-feedback strategies, formulated in terms of tractable strict linear matrix inequalities, which are amenable to efficient numerical implementation via standard Linear Matrix Inequality solvers. The theoretical results not only generalize existing approaches to integer-order systems but also fill a gap in the literature concerning fractional-order large-scale nonlinear systems. Two illustrative numerical examples are presented to validate the proposed methodologies, demonstrating the effectiveness and robustness of the control schemes under various uncertainties and nonlinearities.