Parametric Design of Functional Interval Observer for Time-Delay Systems with Additive Disturbances

Abstract

In this paper, a parametric method to design a functional interval observer (FIO) for time-delay systems with both input and output additive disturbances is investigated. First, a novel definition and sufficient condition for the existence of an FIO are proposed. Inspired by the solution of a class of generalized Sylvester matrix equations (GSEs), completely parameterized expressions of FIO coefficient matrices are established. The parameter matrices in the expressions can be utilized as the design degrees of freedom and optimized to improve the convergence rate of the error system. Finally, a numerical example and a real-world example are presented to demonstrate the effectiveness of the proposed method. KeywordsFunctional interval observer • Time-delay systems • Generalized Sylvester matrix equations • Additive disturbances B Yin-Dong Liu

Time‐dependent Luenberger‐type interval observer design for uncertain time‐varying systems

“…where K(k), U(k), R(k) are the selectable parameters. Then, by assigning R(k) as a Nonnegative and Schur matrix and the rank condition (38), all the solutions to the matrix difference equation set ( 34)-( 36) exist as (37) where the generalized inverse C † (k) can be computed by QR or singular value factorization. 34,35 Finally, according to Theorem 4, the time-dependent Luenberger-type IO, in the form of (33), is constructed with (37).…”

“…However, this forced decoupling condition is valid if (20) has enough design degrees of freedom. Therefore, how to effectively implement the time-dependent Luenberger-type-based interval estimation for (49) (or for the multiple time 30,36,37 and even more complex models) is the focus of our subsequent work and efforts. Meanwhile, the IO parametric forms are built as (15), (16), and (28), how to select the parameters reasonably, namely IO optimization, is still a problem worthy of discussion.…”

“…k) = 0.7, 𝜃 11 (k) = 1, 𝜃 12 (k) = 𝜃 21 (k) = 0, 𝜃 22 (k) = 0, u 11 (k) = 1, u 12 (k) = 0, u 21 (k) = 0, u 22 (k) = 1,and as(37), the coefficient matrices of (33) are determined as…”

A parametric design method of observer‐based state feedback controller for quasi‐linear systems

“…The design of observers for linear systems has attracted great attention and research since Luenberger proposed it in the 1960s [2,3]. For linear systems, observers have been maturely researched and applied [4,5]. Unlike linear systems, which have well-established theoretical development and applications, the design of observers for nonlinear systems is more complicated.…”

Parametric design of reduced-order functional observers for linear time-varying delay systems

“…More related research can be found in the literature. [13][14][15][16][17][18][19] Time-delay phenomena are frequently encountered in many practical systems. It has a significant effect on system performance and may cause instability, oscillation, and so on.…”