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

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 control to permanent magnet synchronous motor via proportional plus integral feedback

This study investigates a parametric approach to design the proportional-integral (PI) controller for a permanent magnet synchronous motor (PMSM). Based on the solutions of the generalized Sylvester equation, the generally parametric expressions of PI controller and right eigenvector matrix are obtained. By using the parametric approach, the closed-loop system is converted into a linear time-invariant system with an expected eigenstructure. Further, a numerical example is put forward to illustrate the effectiveness and feasibility of the proposed parametric approach.

Common solutions of linear equations in a ring, with applications

This paper gives necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair a_1xb_1 = c1, a_2xb_2 = c2, via a simpler equation p_1xp_2 + q_1yq_2=c, when each element belongs to an associative ring with unit. The paper also considers the same problem in the setting of a strongly ∗-reducing ring. Solutions of the generalized Sylvester equation are also presented. Both the solvability conditions and the expression for the general solution are given in terms of inner inverses. The paper uses the results obtained in the ring setting to give equivalent results for operators between Banach spaces, thus also recovering some of the well known matrix results.

A Newton-like method for computing deflating subspaces

This work is devoted to computations of deflating subspaces associated with separated groups of finite eigenvalues near specified shifts of large regular matrix pencils. The proposed method is a combination of inexact inverse subspace iteration and Newton’s method. The first one is slow but reliably convergent starting with almost an arbitrary initial subspace and it is used as a preprocessing to obtain a good initial guess for the second method which is fast but only locally convergent. The Newton method necessitates at each iteration the solution of a generalized Sylvester equation and for this task an iterative algorithm based on the preconditioned GMRES method is devised. Numerical properties of the proposed combination are illustrated with a typical hydrodynamic stability problem.