Constrained solutions of generalized coupled discrete-time periodic matrix equations with application in state observer design for linear periodic systems

Purpose It is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization. Design/methodology/approach The paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm. Findings Through numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma. Originality/value It is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.