A requirement of many multi-input multi-output control and estimation problems is a special structure of the gain matrix. This paper presents a constrained optimal method by which it is possible to constrain some elements of the gain matrix and to optimize the behaviour using the remaining parameters. Only linear constraints are considered and an algorithm based on a modified Riccati equation is obtained. The asymptotic solution for the steady state can be reduced to a sequence of classical Riccati equations by using an iterative approach. Numerical techniques have been found and computer programmes developed. Numerical examples are given.