Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller.     

Squaring down and the problems of almost zeros for continuous-time systems

In this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains. We derive the minimal gain of the precompensator to achieve such a square system. If the gain of this precompensator is too large then we derive an explicit trade-off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system.