An efficient reciprocity and passivity preserving balanced truncation for RLC networks is presented in this paper. Reciprocity and passivity are fundamental principles of linear passive networks. Hence, reduction with preservation of reciprocity and passivity is necessary to simulate behavior of the circuits including the RLC networks accurately and stably. Moreover, the proposed method is more efficient than the previous balanced truncation methods, because sparsity patterns of the coefficient matrices for the circuit equations of the RLC networks are fully available. In the illustrative examples, we will show that the proposed method is compatible with PRIMA, which is known as a general reduction method of RLC networks, in efficiency and used memory, and is more accurate at high frequencies than PRIMA.

In this paper, an infinite-horizon team-optimal incentive Stackelberg strategy is investigated for a class of stochastic linear systems with many non-cooperative leaders and one follower. An incentive structure is adopted which allows for the leader's team-optimal Nash solution. It is shown that the incentive strategy set can be obtained by solving the cross-coupled stochastic algebraic Riccati equations (CCSAREs). In order to demonstrate the effectiveness of the proposed strategy, a numerical example is solved.

In this paper, the H2/H∞ control problem for a class of stochastic discrete-time linear systems with state-, control-, and external-disturbance-dependent noise or (x, u, v)-dependent noise involving multiple decision makers is investigated. It is shown that the conditions for the existence of a strategy are given by the solvability of cross-coupled stochastic algebraic Riccati equations (CSAREs). Some algorithms for solving these equations are discussed. Moreover, weakly-coupled large-scale stochastic systems are considered as an important application, and some illustrative examples are provided to demonstrate the effectiveness of the proposed decision strategies.

In this letter, a computational approach for solving cross-coupled algebraic Riccati equations (CAREs) is investigated. The main purpose of this letter is to propose a new algorithm that combines Newton's method with a gradient-based iterative (GI) algorithm for solving CAREs. In particular, it is noteworthy that both a quadratic convergence under an appropriate initial condition and reduction in dimensions for matrix computation are both achieved. A numerical example is provided to demonstrate the efficiency of this proposed algorithm.