Interval functional observers for time‐delay systems with additive disturbances

Abstract

Summary This article considers the design of interval functional observers to estimate a linear function of the state vector of time‐delay systems subject to both input and output additive disturbances. Two novel functional observers are proposed and designed such that they bound the set of all admissible values of a linear function of the state vector at each instant of time. By contrast to interval observers currently available in the literature, both observers proposed in this article utilize multiple delayed output measurement and have a more general structure. This trade‐off feature overcomes some drawbacks in previous work and enables interval functional observers to be designed for a wider class of time‐delay systems. Conditions for the existence of interval functional observers are derived and an effective design algorithm for computing unknown observer matrices is provided. Two illustrative examples are given to show the advantages and effectiveness of our design method.

Design of distributed event‐triggered states and unknown disturbances observers for time‐varying delay interconnected systems

“…For example, large interconnected power systems, 1 interconnected vehicular system, 2 energy management in DC‐grids, 3 linear transportation networks, 4 DC microgrids, 5 switched interconnected non‐affine nonlinear systems under arbitrary switching, 6 DC bus networks, 7 ecological systems, biological systems and energy systems, 8 industrial processes, 9 electrical circuits 10 . On the other hand, the information on state vectors of dynamical systems plays an important role in many applications such as state‐feedback control, system supervision, fault diagnosis of dynamic processes, and so on (see, for example, References 11–18). However, very often, the information on state vectors is often unavailable due to many reasons such as technical, and economic.…”

Interval observer–based compensators design for linear systems with uncertain time-varying parameters

“…Meanwhile, derived conditions in existing work on interval observer and observer-based controller design have strong coupling structure. Although several interval observer design methods for control systems have reported in the current literature (see survey papers (Cacace et al, 2015; He and Xie, 2020; Huong et al, 2020; Kharkovskaya et al, 2018; Zhu et al, 2023) and the references cited therein), there is still insufficient study on interval observer design based on monotone system theory. Especially, how to design an interval observer gain via separation principle such that design condition for the cooperativity and stability of error dynamics system is still an open research.…”