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In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov… (More)

In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system. The construction of the controller involves solving the full-order algebraic Riccati equation with small parameter ε. Under control-oriented assumptions, we first provide the sufficient conditions such that… (More)

In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be indeÿnite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton–Kantorovich theorem when the initial condition is chosen… (More)

In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a weaker convexity requirement is satisfied; for Ž. instance ᑣ, , -convexity is assumed for both objective and constraint set functions. Some duality models are also discussed. Wolfe-type and Mond᎐Weir-type duality… (More)

In this paper, a group differential game problem is formulated using the system model of multiparameter singularly perturbed systems (MSPS). The case that there exist two groups of players with a conflict interest in the game is considered, and the players in each group must make their own decisions by taking into account the group interest. A method is… (More)