Parametric Iterative Algorithm For Discrete Periodic Sylvester Matrix Equation

Periodic system is a kind of simple time-varying system,which connects timeinvariant system and time-varying system.Many systems in engineering applications can be described by periodic systems,such as satellite attitude control and manipulator motion control.In the field of computer communication,discrete periodic system is very important,because continuous signals should go through discretization process in sampling system before transmission.The first step of studying discrete periodic system is proving that system is stable,and the determination of stability is related to the solution of matrix equation.Therefore,in this thesis,an improved parametric iteration algorithm is proposed for solving the Sylvester matrix equation in the discrete periodic system.The main research contents are as follows.In the thesis,a single parameter iterative algorithm is proposed for solving discrete periodic Sylvester matrix equation.The difference between single parameter algorithm and Smith iterative algorithm lies in the introduction of parameter variables and the latest estimation information.The introduction of the latest estimation information can maximize the usage of iterative information,while the introduction of parameter variables can make the algorithm flexibly adjust the weight of valuation information,which improve the iteration speed of the algorithm.On the other hand,the thesis further proves the convergence condition of the parameter iterative algorithm,verifies the influence of the periodic order of the matrix equation on the convergence speed of the algorithm,and finds a way calculate algorithm's optimal parameters.Finally,simulation results show that the convergence effect of single-parameter iterative algorithm is better than that of Smith iterative algorithm.Based on single parameter iterative algorithm,the thesis proposes multi-parameter iterative algorithm by increasing parameter variables,which makes the adjustment of the algorithm more flexible.Similarly,the basic properties of the algorithm is analyzed in the thesis,including convergence,parameter range and the influence of estimated information on the convergence rate of the algorithm.Due to the increase of parameters,it is difficult to calculate optimal parameters directly.In the thesis,the golden section method is proposed to solve the optimal parameters,where a two-dimensional plane's optimal parameters case is proposed.Finally,simulation results show that the convergence effect of the multiparameter iterative algorithm is better than that of the single parameter iterative algorithm.In the thesis,two other forms of multi-parameter iterative algorithms are proposed,which are named separately the weighted iterative algorithm based on the latest estimation information and the successive over relaxation iterative algorithm based on the latest estimation information.Then the convergence of algorithm above are proved.Finally,the convergence speed of the algorithms is compared by simulation.