*Correspondence to: Z. Gajic, Department of Electrical and Computer Engineering Rutgers University, 94 Brett Road, Piscataway, NJ 08855-0909, U.S.A. OPTIMAL CONTROL APPLICATIONS AND METHODS Optim. Control Appl. Meth., 20, 93}112 (1999) SUBSYSTEM-LEVEL OPTIMAL CONTROL OF WEAKLY COUPLED LINEAR STOCHASTIC SYSTEMS COMPOSED OF N SUBSYSTEMS MYO-TAEG LIM AND ZORAN GAJIC* School of Electrical Engineering, Korea University, Seoul 136-701, South Korea Department of Electrical and Computer Engineering Rutgers University, 94 Brett Road, Piscataway, NJ 08855-0909, U.S.A. SUMMARY In this paper we introduce a transformation for the exact closed-loop decomposition of the optimal control and Kalman "ltering tasks of linear weakly coupled stochastic systems composed of N subsystems. In addition to having obtained N completely independent reduced-order subsystem Kalman "lters working in parallel, we have obtained the exact solution of the algebraic regulator and "lter Riccati equations in terms of the solutions of the corresponding reduced-order subsystem algebraic Riccati equations. The introduced transformation produces a lot of savings especially for on-line computations since it allows parallel processing of information with lower-order-dimensional Kalman "lters. The methodology present- ed is applied to a 17th-order cold-rolling mill. Copyright  1999 John Wiley & Sons, Ltd. KEY WORDS: Decouplig; Order reduction; linear-quadratic regulators; Kalman "lters; algebraic Riccati equation 1. INTRODUCTION Linear weakly coupled systems were introduced to control audiences by Kokotovic and his coworkers in 1969, and since then they have been studied in di!erent set-ups by many control researchers. A decoupling transformation that exactly decouples weakly coupled linear systems composed of two subsystems into independent subsystems was introduced in 1989 by Gajic and Shen. The corresponding optimal Kalman "ltering problem for two subsystems in terms of the reduced- order problems has been studied in Reference 14. The transformation of Gajic and Shen is extended to the general case of linear weakly coupled systems composed of N subsystems by Borno. In this paper, we use the results of Borno in order to extend the previously obtained results to the general optimal control and Kalman "ltering problems of linear weakly coupled stochastic systems composed of N subsystems. The exact closed-loop decomposition technique proposed guarantees complete decoupling of the global optimal Kalman "lter and distribution of all required o!-line and on-line computations. In addition, we will show that the presented methodology is valid for a broader class of linear-quadratic optimal "ltering and CCC 0143 } 2087/99/020093}20$17.50 Received 23 December 1997 Copyright  1999 John Wiley & Sons, Ltd. Revised 29 September 1998