On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case
For control theorists, this work provides a discrete-time analogue of known continuous-time results, but is incremental as it does not introduce new methods or insights beyond the existing continuous-time analysis.
This paper extends the study of connectivity properties of stabilizing feedback gains from continuous-time to discrete-time MIMO LTI systems, showing that the set can have exponentially many connected components.
In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time. Recently, connectivity properties of this set (for continuous time) have been reported in the literature, along with a discussion on how this connectivity is affected by restricting the feedback gain to linear subspaces. We show that analogous to the continuous-time case, one can construct instances where the set of stabilizing feedback gains for discrete time LTI systems has exponentially many connected components.