H/sup /spl infin// control of large scale jump linear systems via averaging and aggregation

This paper studies, under state feedback policies, the H/sup /spl infin// control design for large scale jump linear systems where the form process admits strong and weak interactions. Using averaging and aggregation techniques, an aggregate jump linear system of considerably smaller order has been obtained, along with a corresponding cost function. This reduced-order (aggregate) problem is another piecewise-deterministic H/sup /spl infin// control problem, and based on its solution, we obtain the asymptotic limit of the optimal performance level for the full-order system, as well as an approximate controller that asymptotically achieves any desired performance level for the full-order system. A by product of this analysis is a similar decomposition for the piecewise-deterministic linear-regulator problem.