scholarly journals Extending the CGLS method for finding the least squares solutions of general discrete-time periodic matrix equations

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2503-2520 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Finite Number ◽  
Least Squares ◽  
Control Systems ◽  
Discrete Time ◽  
Conjugate Gradient ◽  
Matrix Form ◽  
Matrix Equations ◽  
Numerical Examples ◽  
Periodic Matrix ◽  
Time Periodic

The periodic matrix equations are strongly related to analysis of periodic control systems for various engineering and mechanical problems. In this work, a matrix form of the conjugate gradient for least squares (MCGLS) method is constructed for obtaining the least squares solutions of the general discrete-time periodic matrix equations ?t,j=1 (Ai,jXi,jBi,j + Ci,jXi+1,jDi,j)=Mi, i=1,2,.... It is shown that the MCGLS method converges smoothly in a finite number of steps in the absence of round-off errors. Finally two numerical examples show that the MCGLS method is efficient.

scholarly journals GRADIENT BASED ITERATIVE ALGORITHM TO SOLVE GENERAL COUPLED DISCRETE-TIME PERIODIC MATRIX EQUATIONS OVER GENERALIZED REFLEXIVE MATRICES

2016 ◽  
Vol 21 (4) ◽  
pp. 533-549 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Iterative Algorithm ◽  
Discrete Time ◽  
State Feedback ◽  
Descriptor Systems ◽  
Matrix Equations ◽  
Numerical Examples ◽  
Periodic Matrix ◽  
Periodic State ◽  
Gradient Based ◽  
Time Periodic

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.

Three types of biconjugate residual method for general periodic matrix equations over generalized bisymmetric periodic matrices

2018 ◽  
Vol 41 (10) ◽  
pp. 2708-2725 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
System Theory ◽  
Finite Number ◽  
Periodic Solutions ◽  
General Type ◽  
Numerical Solutions ◽  
Matrix Equations ◽  
Numerical Examples ◽  
Periodic Matrix ◽  
Bcr Method ◽  
Theoretical Results

As is well known, periodic matrix equations have wide applications in many areas of control and system theory. This paper is devoted to a study of the numerical solutions of a general type of periodic matrix equations. We present three types of biconjugate residual (BCR) method to find the generalized bisymmetric periodic solutions [Formula: see text] of general periodic matrix equations [Formula: see text] The main theorems of this paper show that the presented methods can compute the generalized bisymmetric periodic solutions in a finite number of steps in the absence of round-off errors. We give two numerical examples to illustrate and interpret the theoretical results.

Solving the coupled Sylvester-like matrix equations via a new finite iterative algorithm

2017 ◽  
Vol 34 (5) ◽  
pp. 1446-1467 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Finite Number ◽  
Iterative Algorithm ◽  
Design Methodology ◽  
Matrix Form ◽  
Matrix Equations ◽  
Content Type ◽  
Numerical Examples ◽  
The Matrix ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

Purpose The purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations. Design/methodology/approach In this work, the matrix form of the conjugate direction (CD) algorithm to find the solution X of the coupled Sylvester-like matrix equations: {A1XB1+M1f1(X)N1=F1,A2XB2+M2f2(X)N2=F2,with fi(X) = X, fi(X) = X¯, fi(X) = XT and fi(X) = XH for i = 1; 2 has been established. Findings It is proven that the algorithm converges to the solution within a finite number of iterations in the absence of round-off errors. Finally, four numerical examples were used to test the proficiency and convergence of the established algorithm. Originality/value The numerical examples have led the author to believe that the generalized CD (GCD) algorithm is efficient and it converges more rapidly in comparison with the CGNR and CGNE algorithms.

Sign in / Sign up

Export Citation Format

Share Document