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.

This note constructs a functional observer for second‐order linear time‐varying (SOLTV) systems under framework of second‐order systems. Based on the assumption that the SOLTV system is observable, sufficient conditions for the existence of a second‐order functional observer are proposed. Combined with the solution of generalized Sylvester equation (GSE), the completely parameterized expressions of coefficient matrices of functional observer are proposed, which includes the free parameters representing degrees of freedom, and can be utilized to achieve some additional performance. Further, the design procedure is put forward, whose validity is verified through an example.

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.

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.