A New Relaxative Algorithm for Coupled Riccati Matrix Equations

In this paper, an iterative algorithm for solving coupled algebraic Riccati equations is proposed that has the ad-vantage of fast convergence. Firstly, the importance and related theories of solving the Riccati equation in the control problem of Markovian jumping are introduced, and then mathematical induction is used to prove the mono-tonicity and bounded properties of iterative algorithms, and the method of obtaining the initial matrix of iterative algorithms is given. Also, numerical simulation verifies that the convergence speed of the algorithm is faster than some current algorithms.