An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games

<i>H</i><sub>&#8734</sub> Optimal Control Problems for Jump

“…In the begining we remark the LMI approach for finding the stabilizing solution to (5). Following similar investigations [12] [13] we conclude that the optimization problem (for given k)…”

“…In our investigation we present a few iterative methods for finding the stabilizing solution to (5). Convergence properties of the matrix sequence…”

“…The paper of Lanzon et al [1] is the first where is investigated an algebraic Riccati equation with an indefinite quadratic part in the deterministic case. Further on, the Lanzon's approach has been extended and applied to the algebraic Riccati equations of different types [2]- [5] and for the stochastic case [6]. Many situations in management, economics and finance [7]- [9] are characterized by multiple decision makers/players who can enforce the decisions that have enduring consequences.…”

On the Iterative Solution to H<sub>∞</sub> Control Problems

“…His main essential feature is that the iterative process includes two iterative loops-the out loop and the inner loop. We extend the ideas described by Lanzon et al [1] and Feng and Anderson [6] to propose iterative methods where one matrix sequence is constructed. Here we introduce additional two iterative methods which lead directly to the stabilizing solution.…”

“…In addition, we apply two iterations (6) and (9) for computing the stabilizing solution to (1), where one matrix sequence is established. We perform iteration (6) in two ways "(6) + care" and "(6) + lyap".…”