An explicit solution to polynomial matrix right coprime factorization with application in eigenstructure assignment

In this paper, an explicit solution to polynomial matrix right coprime factorization of input-state transfer function is obtained in terms of the Krylov matrix and the Pseudo-controllability indices of the pair of coefficient matrices. The proposed approach only needs to solve a series of linear equations. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback are investigated. These new solutions are simple, they possess better structural properties and are very convenient to use. An example shows the effect of the proposed results.     

An explicit solution to right factorization with application in eigenstructure assignment

Based on the well-known Leverrier algorithm, a simple explicit solution to right factorization of a linear system is established.This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix.Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback are investigated,and general complete parametric solutions to these two problems are deduced. These new solutions are simple,and possess desirable structural properties which render the solutions readily implementable.An example demonstrates the effect of the proposed results.     

An explicit solution to right factorization with application in eigenstructure assignment

1Proble mfor mulationRight factorization oflinear systems is a basic problemincontrol systems theory,and has important applications inmany analysis and design problems ,such as , robuststabilization [1] ,minimal state space realization [2,3] ,speed servo system design [4] ,synthesis of H_infinitycontrollers [5] ,etc .Furthermore ,it has been shown byDuan and his co_authors that a factorization can be usedtoparameterize all the solutions to a generalized_type ofSylvester matrix equations [6 ~8…     

Spatially-weighted nonnegative matrix factorization with application to temporal psychovisual modulation

Nonnegative Matrix Factorization (NMF), which decomposes a target matrix into the product of two matrices with nonnegative elements, has been widely used in various fields of signal processing. In visual signal processing, the spatially nonuniformed distribution of perceptually meaningful information in image and video frames calls for a kind of Spatially-Weighted NMF (swNMF) that applies location dependent weights into the decomposition problem. In this paper we introduce swNMF solution based on the hierarchical alternating least squares (HALS) approach. Then we exemplify its application to a new information display diagram named temporal psychovisual modulation (TPVM) with comparison with traditional HALS method and baseline algorithm of multiplicative update (MU).