- Title
- Eigenvalue assignment for componentwise ultimate bound minimisation in LTI discrete-time systems
- Creator
- Heidari, Rahmat; Seron, Maria M.; Braslavsky, Julio H.; Haimovich, Hernan
- Relation
- 2013 European Control Conference (ECC 2013). Proceeding of the 2013 European Control Conference, ECC 2013 (Zurich, Switzerland 17-19 July, 2013) p. 2323-2330
- Publisher Link
- http://dx.doi.org/10.1109/AUCC.2013.6697312
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- conference paper
- Date
- 2013
- Description
- We address optimal eigenvalue assignment in order to obtain minimum ultimate bounds on every component of the state of a linear time-invariant (LTI) discrete-time system in the presence of non-vanishing disturbances with known constant bounds. As opposed to some continuous-time cases where ultimate bounds can be made arbitrarily small by applying feedback with sufficiently high gain so that the closed-loop eigenvalues are sufficiently fast, the ultimate bound of a discrete-time system with an additive bounded disturbance can never be made smaller than some set that depends on the disturbance bound, even if all closed-loop eigenvalues are set at zero (the fastest possible in discrete-time). In this context, our contribution is twofold: (a) we single out cases where feedback that may not assign all closed-loop eigenvalues at zero achieves the minimum possible ultimate bound for some component of the system state, and (b) by employing an existing componentwise ultimate bound computation formula, we find a class of systems for which assigning all closed-loop eigenvalues at zero indeed yields minimum ultimate bounds. An intermediate result - and our third contribution - in the derivation of (b) is the obtention of the Jordan decomposition that minimises the componentwise ultimate bound formula employed. © 2013 EUCA.
- Subject
- minimisation; closed loop systems; discrete time systems; eigenvalues and eigenfunctions
- Identifier
- http://hdl.handle.net/1959.13/1335009
- Identifier
- uon:27378
- Identifier
- ISBN:9783033039629
- Rights
- © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
- Language
- eng
- Full Text
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