Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

In this paper, motivated by questions in fault tolerance, we investigate the existence of a compensator which simultaneously renders a given r-tuple of plants internally stable. Sufficient conditions are derived for simultaneous pole-assignability of the generic r-tuple by dynamic output feedback, which are also shown to be necessary (and equivalent to generic stabilizability) in the case where the number of either input or output channels is one. We also derive an upper bound on the order of a simultaneous pole-assigning compensator. If r = l, this reduces to the condition derived by Brasch and Pearson, while if r = 2, this contains the recent theorem by Vidyasagar and Viswanadham. The cases r ≤ 3 are new.