Event-triggered control for stable MMP systems with input saturation using a Bessel-Legendre integral inequality

This paper proposes an event-triggered sampled-data control approach for electrical multi-machine power (MMP) systems with polytopic type input saturation. The proposed approach employs a Bessel-Legendre integral inequality, which is less conservative than traditional integral inequalities such as Jensen’s and Wirtinger-based, to improve the system’s stability condition. The event-triggering condition is periodically verified at each sampling instant, and new measurements and control signals are calculated accordingly. The design criteria are expressed in terms of linear matrix inequalities (LMIs), which ensure asymp-totic stability using Lyapunov stability theory. Moreover , the controllability energy function is utilized to analyze the essential nonlinear dynamics of the system. The proposed approach is validated through simulation studies on the MMP system. The results demonstrate that the approach effectively stabilizes the system while minimizing the control effort. The Bessel-Legendre integral inequality provides a less conservative approach than traditional integral inequalities, resulting in better stability conditions and improved control performance. The use of the controllability energy function in conjunction with the event-triggered control approach provides a comprehensive framework for the control of MMP systems with polytopic type input saturation.