State reconstruction in low-sensitivity design of 3-dimensional systems

The problem to be studied in the paper refers to a general class of the linear time-invariant multivariable three-dimensional (3-D) systems using state feedback. For these types of systems, in order to give a quantitative formulation of the problem, the mathematical model is either assumed or derived. In either case there is always a discrepancy between the actual system and its mathematical model, and sensitivity plays an important role in assessing the behaviour of the system or its components under varying conditions. It is shown that using matrix-minimisation techniques we can derive a set of nonlinear matrix equations which constitute the necessary conditions that must be satisfied for an optimal low-sensitivity solution for a general class of (3-D) multivariable systems. The initial conditions of the system are assumed to be random processes with known mean and covariance matrix.