Quantized Feedback Control For Time-Delay Systems Via Sliding Mode Observers

The paper studies the problem of quantized feedback control for uncertain systems with time-varying delays based on sliding mode observers (SMOs), where the time-varying delays are assumed not to be available at real time. Firstly, in order to construct an SMO, each term on time-varying delay in the plant is estimated by the responding two terms on the lower bound and the upper bound of the time-varying delay. By constructing a new Lyapunov-Krasovskii functional and applying both Wirtinger-type integral inequality and reciprocally convex combination inequality, a delay-dependent condition on designing an SMO is proposed so that the dynamical error system is practically stable. Secondly, based on the designed SMO, a practical stabilizing quantized controller is designed such that the Krasovskii solutions of the closed-loop system exponentially converge to a bounded ellipsoid. Finally, an example is illustrated to demonstrate the effectiveness of the design methodology.