Abstract
In this paper, a parametric approach to design a Luenberger functional observer for linear time-varying (LTV) systems with time-delay is investigated. Based on the solution to generalized Sylvester equation (GSE), the complete general parametric expressions for the functional observer gain matrices are established with the time-varying coefficient matrices, the time-varying closed-loop system and a group of arbitrary parameters. With the parametric method, the observation error system can be transformed into a linear system with the expected eigenstructure. Finally, a numerical simulation is provided to illustrate the effectiveness of the parametric approach.
Highlights
Due to the complex work condition on-site, the state variables cannot be all measured such that it is difficult for the realization of control strategies
The concept of observer design is proposed by Luenberger [1], [2], in which the state of the system is reconstructed to achieve the corresponding control strategy [3]–[5]
The linear function observer has the advantage of greatly reducing the complexity of designing
Summary
Due to the complex work condition on-site, the state variables cannot be all measured such that it is difficult for the realization of control strategies. For linear time-invariant (LTI) systems, Aldeen and Trinh solved the problem of designing a reduced-order function observer [6]. Aimed at LTV systems, the conditions of existence for linear functional observers have been proposed [9]. Different from the general approaches, a parametric approach is proposed to design a linear functional observer via the solution to GSE [11]. There are only a few works focused on designing observers for LTV systems with time-delay [33]–[35]. The main contribution of the present work is to propose a parametric approach to design a linear function observer for LTV systems with time-delay. Rn×r denotes all real matrices of dimension n × r, Rn×r [s] represents all polynomial matrices of dimension n × r with real coefficients, R+, C denote the set of real number and complex number, eig(A) denotes the set of all eigenvalues of matrix A, deg(A(t, s)) denotes the degree of polynomial A(t, s) with respect to variable s, det(A) is the determinant of matrix A and adj(A) is the adjoint matrix of matrix A, σ1 and σ2 represent the highest degree of dij(t, s) and nij(t, s), σ denotes the maximum among σ1 and σ2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
