Parametric design to reduced-order functional observer for linear time-varying systems

Abstract

This article studies the parametric design of reduced-order functional observer (ROFO) for linear time-varying (LTV) systems. Firstly, existence conditions of the ROFO are deduced based on the differentiable nonsingular transformation. Then, depending on the solution of the generalized Sylvester equation (GSE), a series of fully parameterized expressions of observer coefficient matrices are established, and a parametric design flow is given. Using this method, the observer can be constructed under the expected convergence speed of the observation error. Finally, two numerical examples are given to verify the correctness and effectiveness of this method and also the aircraft control problem.

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

“…, l are nonnegative such that l i=0 F i is Hurwitz. Let N (s) and D(s) be a pair of polynomial matrices satisfying RCF (11). Then, the completely parameterized expressions of coefficient matrices of FIO can be obtained as…”

“…be a pair of right coprime polynomial matrices in the form of (12) and satisfy (11). Then, all the solutions V ∈ C q× p and W ∈ C r × p to the GSE (8) are given by…”

“…With the help of the above set of relations, we can now show that the matrices V and W given by ( 13) satisfy the matrix equation (11), that is,…”

“…A state observer provides an estimate of the internal state of a given real system by using the input and output of the real system [20,21] and provides the basis for many practical applications, such as fault detection [24,33], permanent magnet synchronous motor servo systems [19], DC motors [31], spacecraft flying-around [34], ball and beam systems [18], complex dynamic networks [17] and bank-to-turn (BTT) aircraft control systems [11]. Moreover, other researchers have also provided observer-based output feedback control strategies [12,13,32,35,37,38].…”

Functional observer design using the direct method for discrete time-varying linear systems

“…However, up to now, there is no general method available to effectively solve the Sylvester equation, and every approach proposes conditions on the existence and uniqueness of the GSE solution. 14,15 The method based on the parametric solution of the GSE [16][17][18][19][20] has the advantage to provide all the design degrees of freedom, so that additional performances in control system design can be optimised. However, this method requires that the observer eigenvalues are distinct and stable but not fixed in advance.…”