Finite iterative solutions to periodic Sylvester matrix equations

Abstract The problem considered in this paper is to solve periodic Sylvester matrix equations. A new algorithm is presented to derive the least squares solution of the equations. The proposed iteration can converge to the unique solution of the considered matrix equations at finite steps with arbitrary initial condition. A numerical test result is provided to illustrate the convergence and efficiency of the iterative algorithm.

[1]  Zongli Lin,et al.  Unified Gradient Approach to Performance Optimization Under a Pole Assignment Constraint , 2002 .

[2]  M. Hajarian.  Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations , 2015 .

[3]  Ai-Guo Wu,et al.  Iterative solutions to coupled Sylvester-conjugate matrix equations , 2010, Comput. Math. Appl..

[4]  Rita Simões,et al.  Row and column rank partitions under small perturbations , 2012 .

[5]  J. Woude,et al.  A system of real quaternion matrix equations with applications , 2009 .

[6]  Zhuo-Heng He,et al.  Some matrix equations with applications† , 2012 .

[7]  Paul Van Dooren,et al.  Computational methods for periodic systems - An overview , 2001 .

[8]  Guang-Ren Duan,et al.  Gradient based iterative algorithm for solving coupled matrix equations , 2009, Syst. Control. Lett..

[9]  J. Zhou,et al.  Harmonic Lyapunov equations in continuous-time periodic systems: solutions and properties , 2007 .

[10]  Bart De Moor,et al.  Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices , 2016 .

[11]  Jun-e Feng,et al.  On solutions to the matrix equations XB-AX=CY and XB-AX^=CY , 2016, J. Frankl. Inst..

[12]  Bin Zhou,et al.  Parametric Pole Assignment and Robust Pole Assignment for Discrete-Time Linear Periodic Systems , 2010, SIAM J. Control. Optim..

[13]  Zhuo-Heng He,et al.  The general solutions to some systems of matrix equations , 2015 .

[14]  Guang-Ren Duan,et al.  Stability and stabilization of discrete-time periodic linear systems with actuator saturation , 2011, Autom..

[15]  U. Filobello-Niño,et al.  Laplace transform-homotopy perturbation method as a powerful tool to solve nonlinear problems with boundary conditions defined on finite intervals , 2015 .

[16]  Qing-Wen Wang,et al.  Solvability conditions and general solution for mixed Sylvester equations , 2013, Autom..

[17]  James Lam,et al.  Toward solution of matrix equation X = Af (X)B + C , 2011, 1211.0346.

[18]  James Lam,et al.  Pole assignment with eigenvalue and stability robustness , 1999 .

[19]  Guang-Ren Duan,et al.  Numerical solution to linear matrix equation by finite steps iteration , 2010 .

[20]  Zongli Lin,et al.  Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls , 2011 .

[21]  Ai-Guo Wu,et al.  Finite iterative solutions to coupled Sylvester-conjugate matrix equations , 2011 .

[22]  Jianli Zhao,et al.  Finite iterative method for solving coupled Sylvester-transpose matrix equations , 2014 .

[23]  Guangbin Cai,et al.  Solving periodic Lyapunov matrix equations via finite steps iteration , 2012 .

[24]  Qing-Wen Wang,et al.  Systems of coupled generalized Sylvester matrix equations , 2014, Autom..

[25]  Ai-Guo Wu,et al.  Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation , 2011, Appl. Math. Comput..