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This paper considers the decentralized control of a nested linear time-varying (LTV) discrete-time system using a nested LTV controller for an l 2 -induced norm performance criteria. An operator theoretic approach is used to obtain exact conditions for the feasibility of structured linear controller synthesis. These include conditions for the completion of scaling matrices obtained through an updated matrix completion lemma. When individual controller dimensions are chosen at least as large as the plant, these conditions reduce to convex inequalities coupled over time. The completion lemma also provides an algorithm to complete the closed loop scaling matrices leading to inequalities for controller synthesis.

This paper considers an optimal decentralized control problem for a linear system with stochastically switched input/output matrices depending on local parameters. These stochastic parameters are assumed independent in time and available instantaneously to the local controller but with a one time step delay to the other. We first solve this problem for the case of a single time step and show that the optimal policy can be reached through iterating the best responses of each player. For the optimal multiple step problem, a dynamic programming approach is employed while using the result of the one step control at each step.

This paper investigates an optimal decentralized control problem for a system with B-matrices dependent on stochastic parameters. It is assumed that these parameters are independent in time and available locally to each controller. The objective is to find a decentralized state feedback control policy that minimizes a multi step quadratic cost function. We first solve this problem for the case of one time step and show that the optimal policy can be reached through iterating the best responses of each player. For the optimal multiple step problem, a dynamic programming approach is employed while using the result of the one step control at each step. Finally in the infinite horizon case, we provide sufficient conditions under which the optimal control policy is unique and stabilizes the system in a mean square sense.

In this paper we consider spatially distributed heterogeneous discrete-time systems which are interconnected over an infinite lattice. An operator-pencil approach is employed to develop analysis conditions, which are less conservative than those previously available. Synthesis conditions are also obtained and are in the form of operator inequalities. In general these are infinite dimensional but in the case of eventually invariant systems these reduce to a semidefinite program.