Observer-Based H∞ Control for Uncertain Neutral Systems with Distributed Delays

This paper addresses the observer-based H∞ control problem for a class of uncertain neutral systems with distributed delays subject to norm-bounded time-varying uncertainties and bounded time-varying delays. Since complete state measurements are often unavailable in practical systems, an observer-based framework is employed to estimate inaccessible states and facilitate controller implementation. To enhance robustness against uncertainties and disturbances, an integral sliding mode control approach is adopted. By constructing an appropriate Lyapunov–Krasovskii functional that simultaneously characterizes the observer and estimation-error dynamics, novel delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs). Based on these conditions, a sliding mode control law is developed to ensure the reachability of the prescribed sliding surface, while an observer-based controller is designed to guarantee the robust asymptotic stability of the resulting closed-loop system and achieve a prescribed H∞ performance level. Finally, numerical examples are presented to illustrate the effects of the distributed delays on the considered system and to validate the effectiveness and applicability of the proposed method. Moreover, the proposed results are shown to reduce conservatism and improve computational efficiency compared with existing results reported in the literature.