Abstract
In this paper, we are concerned with the optimization of observations in stationary LQG stochastic control systems which employ the stationary Kalman filter. The performance of the LQG stochastic control system is dependent on the gain matrix in the linear observation. From the view point of the performance of the LQG regulator, it is better to take the dimension and the value of this gain matrix as large as possible. However, it is usually the case that we cannot take these values so large but there exist certain physical restrictions. By taking a performance criterion for the selection of the gain matrix as a quadratic function on the estimation error and the gain matrix and by introducing the eigenvalues-eigenvectors representation of a nonnegative definite symmetric matrix, the condition of optimality is derived under weaker assumptions than already known. Also, numerical calculations are easily carried out by introducing an n-dimensional polar coordinates system.
