New sliding mode observer design method for a class of time-varying delay systems with matched and unmatched uncertainties

This paper concerns with a new design method of a sliding mode observer (SMO) for a class of linear uncertain time-varying delay systems. This new method builds on the current SMO design methods for linear uncertain systems, but it gives a robust state estimation in spite of the presence of both uncertainties and time delay. In the meantime, the considered uncertainties are matched and unmatched, and the time delay is constant and affects the state system. The basic idea in the design consists to combine the SMO concept with a Lyapunov-Krasovskii functional which is numerically tractable via linear matrix inequalities (LMIs) optimisation. This design approach ensures the stability of the system estimation error. In addition, the dynamic properties of the observer are analysed and the reachability condition is satisfied. A DC-8 aircraft system is included to illustrate the validity and the applicability of the proposed approaches. Copyright © 2024 Inderscience Enterprises Ltd.