ITERATIVE ALGORITHMS FOR THE GENERALIZED DISCRETE-TIME PERIODIC SYLVESTER TRANSPOSE MATRIX EQUATIONS WITH APPLICATION IN THE PERIODIC STATE OBSERVER DESIGN OF LINEAR SYSTEMS

In this work, four iterative algorithms are provided for solving generalized discrete-time periodic Sylvester transpose matrix equations. Based on the Jacobi iterative algorithm and hierarchical identification principle, the present work provides the full-row rank Jacobi gradient iterative (RRJGI) algorithm, the full-row rank accelerated Jacobi gradient iterative (RRAJGI) algorithm, the full-column rank Jacobi gradient iterative (CRJGI) algorithm and the full-column rank accelerated Jacobi gradient iterative (CRAJGI) algorithm. The convergence of the algorithms are proved, and it is concluded that the proposed iterative methods are convergent under certain conditions for arbitrary initial matrices. Numerical results show the feasibility of the proposed algorithms and its superiority compared with other algorithms. Finally, an application example for the periodic state observer design of linear systems is given.