We show that 2-norm pseudospectra of m-by-n matrices have no more than 2m(4m-1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu's recent algorithm, and we show how these may be used to locally maximize the distance to uncontrollability for a parameterized system.
- Connected components
- Distance to uncontrollability
- Robust control
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