Quasi-data-driven static output feedback control of linear systems with input and state delays

Abstract

This paper presents a quasi-data-driven static output feedback (SOF) control framework for discrete-time linear systems subject to time-varying state and input delays. The proposed controller synthesis leverages input-state-output data acquired from the open-loop system, integrated with delay-dependent data-based Linear Matrix Inequality (LMI) conditions derived using Lyapunov–Krasovskii stability theory. A salient feature of this methodology is its ability to compute controller gains without prior knowledge of the system dynamics, thereby eliminating the dependence on explicit mathematical models. Furthermore, a data-driven reference-tracking input scheme is developed for time-delay systems, addressing piecewise-constant reference trajectories while guaranteeing asymptotic stability of the tracking error. The efficacy of the proposed approach is rigorously validated through numerical simulations and also experimental implementation on a twin-rotor system for pitch angle tracking, demonstrating robust performance in both theoretical and practical settings.