One often encounters numerical difficulties in solving linear matrix inequality (LMI) problems obtained from H∞ control problems. We discuss the reason from the viewpoint of optimization. It is empirically known that a numerical difficulty occurs if the resulting LMI problem or its dual is not strongly feasible. In this paper, we provide necessary and sufficient conditions for LMI problem and its dual not to be strongly feasible, and interpret them in terms of control system. For this, facial reduction, which was proposed by Borwein and Wolkowicz, plays an important role. We show that a necessary and sufficient condition closely related to the existence of invariant zeros in the closed left-half plane in the system, and present a way to remove the numerical difficulty with the null vectors associated with invariant zeros in the closed left-half plane. Numerical results show that the numerical stability is improved by applying it.
|Number of pages||7|
|Publication status||Published - Jul 1 2015|
|Event||8th IFAC Symposium on Robust Control Design, ROCOND 2015 - Bratislava, Slovakia|
Duration: Jul 8 2015 → Jul 11 2015
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering