LAPACK-Based Condition Estimates for the Discrete-Time LQG Design

The Linear-Quadratic Gaussian (LQG) design is the most efficient and widely used design approach in the field of linear stochastic control systems. From theoretical point of view this approach is reduced to the synthesis of a LQ state regulator and of a Kalman filter for the controlled system. From computational point of view the LQG design consists of solving a pair of matrix Riccati equations: one for the LQ regulator design and a second one (dual to the first Riccati equation) for the Kalman filter design. In this paper we present reliable algorithms for estimation of condition numbers of the discrete Riccati equations in the discrete-time LQG design. Efficient LAPACK-based condition estimators are proposed involving the solution of triangular Lyapunov equations along with one-norm computation.