Stabilising compensators for linear time-varying differential systems

ABSTRACT

In this paper, we describe a constructive test to decide whether a given linear time-varying (LTV) differential system admits a stabilising compensator for the control tasks of tracking, disturbance rejection or model matching and construct and parametrise all of them if at least one exists. In analogy to the linear time-invariant (LTI) case, the ring of stable rational functions, noncommutative in the LTV situation, and the Kučera–Youla parametrisation play prominent parts in the theory. We transfer Blumthaler's thesis from the LTI to the LTV case and sharpen, complete and simplify the corresponding results in the book ‘Linear Time-Varying Systems’ by Bourlès and Marinescu.

KEYWORDS:

• Behaviour
• time-varying
• stabilising compensator
• tracking
• disturbance rejection
• model matching
• exponential stability

AMS-classification:

• 93B52
• 93D15
• 93B25
• 93C05
• 93D20
• 34H15

Acknowledgements

The author thanks the two reviewers for their efforts and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.