Minh T. Tran

Reduced order discrete-time models

Linear shift-invariant discrete-time systems satisfying the two time scale property-are considered. Conditions for a complete separation of slow and fast subsystems are given. Subsystem regulator problems are investigated and the controllability property of the system is established based on the subsystem controllability properties. A subsystem controller design method is proposed depending on the separability of the slow and fast controls.

A note on the discrete Lyapunov and Riccati matrix equations

Abstract Inequalities which are satisfied by the determinants of the positive definite solutions of the discrete algebraic Riccati and Lyapunov matrix equations are presented. The results give lower bounds for the product of the eigenvalues of the matrix solutions. Also for a discrete Lyapunov equation, an algorithm is presented to determine under what conditions a positive diagonal solution will exist. If all the conditions are satisfied, the algorithm also provides such a diagonal solution.

Nash strategies for discrete-time systems with slow and fast modes

Linear shift invariant discrete-time Nash games are considered. In particular, linear-quadratic infinite-time zero-sum Nash games for discrete-time systems with slow and fast modes are investigated. Derivation of near-optimal strategies which do not require any knowledge of the small singular perturbation parameter is presented based on the asymptotic behaviour of the solution.

Stackelberg strategies in discrete linear quadratic problems

Linear closed-loop Stackelberg strategies in sequential decision-making problems for linear time-invariant discrete systems and trace criteria which may be interpreted as the expected value of quadratic criteria are considered. Necessary conditions for the solution are developed and an algorithm of the multi-level Stackelberg problem is presented. An example for a two-level problem is presented to illustrate the proposed numerical algorithm

On the Discrete Riccati Matrix Equation

In this note, the inequality which is satisfied by the determinant of the positive definite solution of the discrete algebraic Riccati matrix equation is presented. The result gives lower bound for the product of the eigenvalues of the matrix solution.