Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer res...

New perturbation theorems are proved for simultaneous bases of singular subspaces of real matrices. These results improve the absolute bounds previously obtained in [6] for general (complex) matrices. Unlike previous results, which are valid only for the Frobenius norm, the new bounds, as well as those in [6] for complex matrices, are extended to any unitarily invariant matrix norm. The bounds ...

By virtue of an operator-theoretical approach, we deal with hyperbolic singular perturbation problems for integrodifferential equations. New convergence theorems for such singular perturbation problems are obtained, which generalize some previous results by This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, an...

In this paper, we study the sensitivity and second order perturbation expansions of simple nonzero finite generalized singular values of a complex matrix pair, which is analytically dependent on several parameters. Our results generalize the perturbation analysis given by Sun [J. Comput. Math., 6 (1988), pp. 258–266] for simple nonzero singular values.

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

In this paper robust PID control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. In dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. To develop the idea of control for cable robots with elastic cables, a robust PID control for cable driven robots with ideal rigid cables is firstly de...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are...