Reference management-based resilient control for delayed periodic piecewise polynomial systems under proportional integral observer

This article examines the proportional integral observer (PIO)-based resilient tracking control problem for periodic piecewise polynomial systems (PPPSs) in the presence of time delay and disturbances. To be precise, the PPPSs are formulated by dividing the fundamental period of periodic systems into numerous subintervals, each of which is defined using matrix polynomial functions. Further, the PIO strategy is employed to estimate the states of the undertaken system with high precision wherein the integral term in PIO enhances the system's design flexibility and also increases its robustness. Taking advantage of these characteristics, a PIO-based tracking control is configured with gain perturbations to track the desired reference states. Moreover, to attenuate the implications made by disturbances in considered system design, $ H_\infty $ H∞ performance is employed. Furthermore, in order to establish adequate conditions in the form of linear matrix inequalities, the time-varying polynomial Lyapunov–Krasovskii functional is implemented. Then, the time-varying gain matrices of the control scheme and PIO configuration are computed by solving the obtained criteria through the MATLAB platform. Concludingly, to evidence for the discoveries' potential and usefulness, a numerical example is offered.