On L/sup 2/-sensitivity minimization of linear state-space systems

Properties of the solution to the L/sup 2/-sensitivity minimization problem are discussed. In particular, a specific form of the solution is derived together with a bound. This bound gives an insight into the difference between a pure L/sup 2/-sensitivity optimal realization, and a mixed L/sup 2//L/sup 1/-sensitivity optimal one. The question of L/sup 2/-sensitivity balanced truncation is addressed, and a counterexample is presented to show that two main properties associated with model reduction by truncating a Lyapunov balanced realization are lost in the case of L/sup 2/-sensitivity balanced truncation.<>