Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

Abstract

ABSTRACTThe problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ε-convergent, which means that the estimate converges robustly within an ε-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov–Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ε-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ε. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.