On the sensitivity of generalized state-space systems

The synthesis of minimum-sensitivity state-space realizations of linear time-invariant systems is a well understood problem. Such realizations have been linked to balanced realizations. The theory is extended to the synthesis of minimum-sensitivity generalized state-space models for singular linear systems. A scalar sensitivity measure is defined, and the minimization of the measure over all admissible realizations is considered. Since minimal realizations are not required to be related by a similarity transformation, the optimization problem is more complex. A criterion is given for determining optimal sensitivity structures. In the nonsingular case, the criterion reduces to the familiar result. The simple example of the right-shift operator is considered