An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices

Dehghan, Mehdi; Hajarian, Masoud

doi:10.1016/j.apm.2009.06.018

Cited by 134 publications

(37 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on the above corollary, we can see that if the solution to the Lyapunov equation (8) is solved efficiently (for related approach, see [11][12][13]15] and the references therein), N (P) is the most convenient way for characterizing the unobservable subspace.…”

Section: Corollary 2 the Linear System (1) Is Observable If And Onlymentioning

confidence: 98%

“…generated by the above iteration can be written explicitly as −1 ), namely, the corresponding results to Lemmas 2-3 and Theorem 1 are trivial for discrete-time system. Therefore, in the following, we only consider the relationship between the unobservable subspace and solutions to the Lyapunov equation (15). (15) is…”

Section: Discrete-time Casementioning

confidence: 99%

“…Let P be the solution to the Lyapunov equation (15). Then the discrete-time system (14) is observable if and only if P > 0 (see, for example, [2]).…”

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Lyapunov iteration and equation characterizations for unobservable subspace

Wang

2010

Applied Mathematics Letters

View full text Add to dashboard Cite

a b s t r a c tThis note is concerned with the unobservable subspace of a linear system and some Lyapunov iteration and equations. It is shown that the unobservable subspace can be characterized by the Lyapunov iteration and equations defined in the paper. The results generalize some standard results on this topic and are expected to take fundamental functions in control system theory. Both continuous-time and discrete-time systems are considered. Numerical examples show the effectiveness of the proposed results.

show abstract

Section: Corollary 2 the Linear System (1) Is Observable If And Onlymentioning

confidence: 98%

Section: Discrete-time Casementioning

confidence: 99%

See 1 more Smart Citation

Lyapunov iteration and equation characterizations for unobservable subspace

Wang

2010

Applied Mathematics Letters

View full text Add to dashboard Cite

show abstract

“…Recently, Dehghan and Hajarian [26][27][28][29][30] proposed some e.cient methods to solve several linear matrix equations over re.exive, anti-re.exive and generalized bisymmetric matrices. In [31], two iterative algorithms were proposed for .nding the Hermitian re.exive and skew-Hermitian solutions of the Sylvester matrix equation AX + XB = C, respectively.…”

Section: Introductionmentioning

confidence: 99%

Solving the generalized sylvester matrix equation Σ i=1 p AiXBi + Σ j=1 q CjYDj=E over reflexive and anti-reflexive matrices

Dehghan

Hajarian

2011

Int. J. Control Autom. Syst.

Self Cite

View full text Add to dashboard Cite

A matrix n n P × ∈ » is called a generalized reflection if T P P = and P 2 =I. An n n × matrix A is said to be a reflexive (anti-reflexive) with respect toIn the present paper, two iterative methods are derived for solving the generalized Sylvester matrix equation ∑ ∑(including the Sylvester and Lyapunov matrix equations as special cases) over reflexive and anti-reflexive matrices respectively. It is proven that the iterative methods, respectively, consistently converge to the reflexive and anti-reflexive solutions of the matrix equation for any initial reflexive and anti-reflexive matrices. Finally, a numerical example is given to demonstrate the effectiveness of the derived methods.

show abstract

“…The applications of linear matrix equations have motivated both mathematicians and engineers to construct methods catering to solve linear matrix equations [1,4,6,7,8,9,19,23,25]. Based on Smith iterations [24], iterative methods were developed for periodic standard Lyapunov matrix equations and projected generalized Lyapunov matrix equations [27,28].…”

Section: Introductionmentioning

confidence: 99%

Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations Over Generalized Reflexive Matrices

Hajarian

2016

Mathematical Modelling and Analysis

Self Cite

View full text Add to dashboard Cite

Abstract. The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm.

show abstract

An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices

Cited by 134 publications

References 42 publications

Lyapunov iteration and equation characterizations for unobservable subspace

Lyapunov iteration and equation characterizations for unobservable subspace

Solving the generalized sylvester matrix equation Σ i=1 p AiXBi + Σ j=1 q CjYDj=E over reflexive and anti-reflexive matrices

Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations Over Generalized Reflexive Matrices

Contact Info

Product

Resources

About