On L2-sensitivity minimization of linear state-space systems

Properties of the solution to the L²-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 L²-sensitivity optimal realization, and a mixed L²/L¹-sensitivity optimal one. The question of L²-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 L²-sensitivity balanced truncation