离散时间Itˆo 型跳变系统Lyapunov 方程的有限次迭代求解算法

针对离散时间Itˆo 型马尔科夫跳变系统Lyapunov 方程的求解给出一种迭代算法. 经证明, 在误差允许的范围内, 该算法可以在确定的有限次数内收敛到系统的精确解, 收敛速度较快, 具有良好的数值稳定性, 并且该算法为显式迭代, 可避免迭代过程中求解其他矩阵方程对结果精度产生的影响. 最后通过一个数值算例对该算法的有效性进行了验证.

Finite iterative algorithm for solving Lyapunov equations of Itˆo stochastic systems with Markovian jumps

An iterative algorithm is given to find an exact solution to the coupled Lyapunov matrix equations of the discrete-time Itˆo stochastic liner systems with Markovian jumps. It has been proved that the algorithm can obtain the solution within finite steps in absence of round-off errors, and has fast convergence speed and good numerical stability. The algorithm is explicit iteration, which avoids the influence of the errors generated during the process of solving the other matrix equations. Finally, a numerical example is given to illurstrate the effectiveness of the proposed algorithm