Design of proportional integral observer-based resilient control for periodic piecewise time-varying systems: The finite-time case

The prime intent of this study is to scrutinize the state estimation and finite-time (FT) stabilization problems for a class of periodic piecewise time-varying systems (PPTVSs) in the presence of external disturbances, immeasurable states and gain fluctuations by dint of resilient control. Moreover, the proportional integral observer system is built in line with the output of the PPTVSs to reconstruct the states of the PPTVSs, since the state dynamics of the system are often not measurable. Meanwhile, the output signals are quantized with the use of a logarithmic quantizer prior to being fed into the constructed observer systems. Further, the fluctuations in the controller and observer gain matrices are considered to occur in a random manner and they pursue the pattern of a Bernoulli distributed white sequence. Subsequently, by means of Lyapunov stability theory and the matrix polynomial lemma, the adequate requirements for ascertaining the FT boundedness and IO-FT stabilization of the addressed system are procured in the context of linear matrix inequalities. Thereupon, on the premise of the established criteria, the gain matrices of the controller and observer are obtained. Ultimately, the simulation results have been showcased including the mass spring damper system to exemplify the efficacy and usefulness of the theoretical conclusions drawn.