Dr Chris Guiver C.Guiver@napier.ac.uk
Lecturer
A stability theorem for the feedback connection of two (possibly infinite-dimensional) time-invariant linear systems is presented. The theorem is formulated in the frequency domain and is in the spirit of combined passivity/small-gain results. It places a mixture of positive realness and small-gain assumptions on the two transfer functions to ensure a certain notion of input-output stability, called Sobolev stability (which includes the classical L2-stability concept as a special case). The result is more general than the classical passivity and small-gain theorems: strong positive realness of either the plant or controller is not required and the small gain condition only needs to hold on a suitable subset of the open right-half plane. We show that the “mixed” stability theorem is applicable in settings where L2-stability of the feedback connection is not possible, such as output regulation and disturbance rejection of certain periodic signals by so-called repetitive control.
Guiver, C., Logemann, H., & Opmeer, M. R. (in press). A mixed passivity/small-gain theorem and its application to output regulation for passive systems. SIAM Journal on Control and Optimization,
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 1, 2024 |
Deposit Date | Aug 1, 2024 |
Print ISSN | 0363-0129 |
Electronic ISSN | 1095-7138 |
Publisher | Society for Industrial and Applied Mathematics |
Peer Reviewed | Peer Reviewed |
Keywords | Feedback control, Output regulation, Passivity theorem, Positive realness, Small-gain theorem, Sobolev stability |
Publisher URL | https://www.siam.org/publications/siam-journals/siam-journal-on-control-and-optimization/ |
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