Abstract
AbstractThis paper discusses dynamic games for a class of linear stochastic delay systems governed by Itô's stochastic differential equation. The Pareto and Nash strategies are developed by solving cross‐coupled matrix inequalities. To obtain these strategy sets, new cross‐coupled algebraic equations (CSAEs) are established on the basis of the Karush‐Kuhn‐Tucker (KKT) conditions, which constitute the necessary conditions. It is noteworthy that the state feedback strategies can be obtained by solving the linear matrix inequality (LMI) recursively. Finally, a numerical example showing the effectiveness of the proposed methods and the attained cost bounds is described.
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