Functional observer design using linear matrix inequalities

Transactions of the Institute of Measurement and Control

2022

This paper investigates the problem of the functional interval observer design for linear time-varying (LTV) systems with additive disturbances in both input and output channels. First, sufficient conditions for the existence of a functional interval observer for LTV systems are proposed. Based on the solution of a type of Sylvester matrix equations (generalized Sylvester equations, GSEs), completely parameterized expressions of functional interval observer coefficient matrices are established, yielding a simple and effective design approach for solving the interval estimation issue of the LTV system, while the free parameters in the expressions provide the design degrees of freedom that can be utilized to achieve additional system specifications. Furthermore, the developed observer may execute state estimation at the desired convergence rate, considerably improving estimate performance. Finally, a numerical example and a back-to-turn (BTT) aircraft control example are presented, with the results showing that the upper and lower bounds provided by the designed observer provide a better performance of interval estimation of the functional state variables, demonstrating the effectiveness of the proposed method.

Section: Introductionmentioning

confidence: 99%

Functional interval observer design for linear time-varying systems with additive disturbances

Sun

Transactions of the Institute of Measurement and Control

2022

“…26 Volkov and Demyanov proposed a design method of functional observers based on LMIs under nonsingular transformation. 27 For complex systems, Ahlem et al proposed an adaptive functional observer design method for multiple discrete time-delay bilinear systems. 28 For the observers of the two-dimensional systems described by the second model of Fornasini-Marchesini local state space, Xu et al obtained the necessary and sufficient condition for the existence of an asymptotic functional observer.…”

Section: Introductionmentioning

confidence: 99%

Reduced‐order functional observers for descriptor linear time‐invariant systems: a parametric method

Sun

Adaptive Control & Signal

2021

This article introduces the parametric design method of the reduced-order functional observer for descriptor linear time-invariant systems. First, existence conditions of reduced-order functional observers are provided. Then, based on the solution of generalized Sylvester equations, completely parameterized expressions of the coefficients matrices of the reduced-order functional observer are established, and the design algorithm of the reduced-order functional observer is also proposed. The advantage of the proposed design method is that the observation error system can be transformed into a linear system with an expected eigenstructure. Finally, two examples are given to verify the effectiveness of the proposed method.

“…A method to construct a minimum-order functional observer is proposed and extended to a system with vector output by Korovin et al [7]. Volkov and Demyanov proposed a novel approach to design functional observers via the solution to linear matrix inequalities (LMIs) [8]. Aimed at LTV systems, the conditions of existence for linear functional observers have been proposed [9].…”

Section: Introductionmentioning

confidence: 99%

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

Yang³

2020

IEEE Access

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. INDEX TERMS Functional observers, LTV systems with time-delay, parametric method, Sylvester equation.