Observer Design for a Time Delay System via the Razumikhin Approach

Abstract

The paper presents an algorithm for the observer design for linear systems with time delay. The observer design is based on a solution of a set of linear matrix inequalities. They are derived using the Razumikhin functional. Quantization effects on the observation error are also studied, a bound on the observation error caused by quantization is derived.Two illustrative examples are presented.

Observer‐based trajectory control for directional drilling process

“…Due to the existence of the lag terms z i (ξ − τ 1 ) and z i (ξ − τ 2 ) in (13), it is usually challenging to ensure the stability of the observer by selecting the gain matrix L i only with the pole placement method [23,24]. The lag terms affect the observer error converging to zero quickly, so the state estimate cannot accurately reflect the actual value [25,26].…”

“…and combining (30) and (32) yields the LMI (23). Meanwhile, the controller and observer gains give, that is, (25).…”

Consensus of a multi-agent systems with heterogeneous delays

“…Complex networks composed of more general agents are investigated in [11] for both continuous and discrete-time cases. The leader-following problem of multi-agent systems with constant delays is solved in [8], the approach based on the Razumikhin functional (for its definition, see e.g [20]) is used. A solution of this problem via the Lyapunov-Krasovskii functional is described in [9].…”

Finite element-based observer design for nonlinear systems with delayed measurements

“…State reconstruction if measurements are quantized is investigated in [15] together with analysis of the impact of imprecisely known value of the delay. An observer for a special case of nonlinear time delay systems -namely for polynomial systems timedelay systems -is proposed in [14].…”