Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

One Concave-Convex Inequality and Its Consequences

Our starting point is an integral inequality that involves convex, concave and monotonically increasing functions. We provide some interpretations of the inequality, in terms of both probability and terms of linear functionals, from which we further generate completely monotone functions and means. The latter application is seen from the perspective of monotonicity and convexity.

Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays

This paper is associated with the problem of robust stability of discrete-time systems with time-varying delays and finite wordlength nonlinearities. The main contribution of the paper is two-fold. First, this paper presents a new Lyapunov function based on the idea of partitioning the delay interval into subintervals. The approach may be considered as an advancement over the several existing approaches where only the lower delay bound is partitioned. The second is that reciprocally convex inequality (RCI) and Wirtinger-based inequality (WBI) are used to estimate the sum terms involved in the forward difference of Lyapunov function. The intermediate delay is also included in the Lyapunov function to deal with the delay information more effectively. Finally, several examples are provided to illustrate the less conservatism of the proposed approach as compared to several existing results.