The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH. Then, recent results on bilateral Diophantine equation are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditio...

Abstract—A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitraril...

In this work, the direct position kinematics of a 3 degree-of-freedom parallel manipulator with three identical limbs, type revolute-prismatic-spherical (RPS), is analyzed. In contrast to the previous studies on this class of manipulators, the revolute joints of the proposed manipulator are actuated rather than the prismatic joints. Direct position kinematics of the manipulator leads to a syste...

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflex...

A unified deflating subspace approach is presented for the solution of a large class of matrix equations, including Lyapunov, Sylvester, Riccati and also some higher order polynomial matrix equations including matrix m-th roots and matrix sector functions. A numerical method for the computation of the desired deflating subspace is presented that is based on adapted versions of the periodic QZ a...

In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

The SST decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. In this topic we are going to consider vectors as fuzzy vectors. We have considered a numerical example and tried to find out solution vector x in fuzzified form using method of SST decomposition.

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generali...

Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems.Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values.The eigenstructureassignmentalgorithmcan be dividedinto two groups, that is, the null space approach and Sylvester equation approach.The null spaceapproachis used to solvemode decoupling proble...