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.
Highlights
In reality, not all state variables can be directly measured, it is for this reason that observers are required to reconstruct the state
Linear time-varying (LTV) system is a type of system whose characteristics change with time, so it can reflect the strong dependence of object characteristics on time more accurately than the traditional timeinvariant system
Based on the results of the fully parameterized solution of generalized Sylvester equation (GSE) proposed in Zhou and Duan,[32] this study investigates the problem of state reconstruction for LTV models
Summary
Not all state variables can be directly measured, it is for this reason that observers are required to reconstruct the state. Rotella and Zambettakis[24] proposed an algorithm to design single-FO for LTV systems, and obtained the minimum order of the observer through iteration under the existing conditions. Wang and Jiao[27] proposed a general adaptive fuzzy smooth dynamic controller to solve the output tracking problem of a class of switched nonlinear systems by designing an appropriate reduced-order observer and introducing fuzzy approximation. Completely parameterized expressions of the gain matrices of the ROFO are established by using the parametric solutions of the GSE proposed above, and the following theorem is given. Find the parametric solutions of matrices T^1(t) and W^ (t) of form (32) with the known matrix F(t), select the parameter Z(t) satisfying equation (42). Compute gain matrices according to equation (31) to complete the construction of reduced-order functional observer. 0 (À t) ð43Þ and we will design the ROFO which can asymptotically tracks the functional signal (4) with
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