Adaptive state observation of linear time‐varying systems with switching unknown parameters: Application to gain scheduling and event‐triggered control

Abstract

SummaryMotivated by its application in gain scheduling and event‐triggered controllers we propose in this paper an adaptive observer for linear time‐varying (LTV) systems with unknown switching parameters, but known switching time instants. To construct the observer we propose an extension to the generalized parameter estimation‐based observers (GPEBO), which we combine with the least‐squares plus dynamic regression extension and mixing (LS+DREM) estimator recently proposed. We prove that the system state and the parameters converge in finite time inside each switching sub‐interval, under the weak assumption of interval‐excitation (IE). The excellent performance of the proposed observer is illustrated with a practical and an academic example both reported in the literature.