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.

Construction of the Fuchs equation with four given finite critical points and a given reducible monodromy group in the resonance case

One inverse problem of the analytic theory of linear differential equations is considered. Namely, the completely integrable Fuchs equation with four given finite critical points and a given reducible monodromy group of rank 2 on the complex projective line is constructed. Reducibility of the monodromy group of rank 2 means that 2×2-monodromy matrices (the generators of the monodromy group) can be simultaneously reduced by a linear nonsingular transformation to an upper triangular form. In so doing we study the case when the eigenvalue ξj of the diagonal matrix of the monodromy formal exponent at a corresponding Fuchs critical point is equal to an integer different from zero (resonance takes place).

Linear Time-Varying Dynamic Systems Optimization via Higher-Order Method: A Sub-Domain Approach

A new procedure for optimization of linear time-varying dynamic systems has been proposed that uses transformations to embed the dynamic equations explicitly into the cost functional. This leads to elimination of Lagrange multipliers and characterization of the optimality equations by high-order differential equations in the same number of variables as number of control inputs. This procedure requires that the transformation matrix be nonsingular at all time within the domain. This paper extends this procedure to problems where a single nonsingular transformation matrix does not exist over the entire domain. In this paper, the time domain is partitioned into intervals such that a nonsingular transformation exists over each interval. The transformations are used to embed the dynamic equations into the cost functional. Variational analysis of the unconstrained cost functionals results in the optimality equations, which are solved efficiently by weighted residual methods. [S0739-3717(00)00601-2]

Compactness of Invariant Densities for Families of Expanding, Piecewise Monotonic Transformations

Let I = [0,1] and let be the space of all integrable functions on I, where m denotes Lebesque measure on I. Let ∥ ∥1 be the ℒ-1-norm and let be a measurable, nonsingular transformation on I. Let denote the space of densities. The probability measure μ is invariant under τ if for all measurable sets A, The measure μ is absolutely continuous if there exists an such that for any measurable set A We refer to ƒ* as the invariant density of τ (with respect to m). It is well-known that ƒ * is a fixed point of the Frobenius-Perron operator defined by

Generalized characteristic functions for simultaneous linear differential equations with variable coefficients applied to propagation in inhomogeneous anisotropic media

A wide class of physical problems can be reduced to sets of simultaneous linear differential equations with variable coefficients. For critical coupling regions of the independent variable where the characteristic values of the coefficient matrix tend to merge, the standard technique employing similarity transformations does not convert the original set of differential equations into a form that is suitable for numerical computations. For these critical coupling regions we employ a nonsingular transformation matrix associated with variable characteristic values to convert the original equation to a form that can be more readily resolved analytically (using an iterative approach) or numerically. The method developed is applied to problems of radio wave propagation in inhomogeneous, anisotropic, dissipative media with critical coupling regions.

A characterization of unitary operators induced by nonsingular transformations and its applications

In this paper we give a necessary and sufficient condition for a unitary operator on an L2-space to be induced by a nonsingular transformation and its applications.