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Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes

Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes
Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes
Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model.
220-233
Dabkowski, P
70e4f9ba-9370-45f9-b409-cccc563a2d8c
Galkowski, K
65b638be-b5a5-4e25-b1b8-e152c08a1cbb
Bachelier, O
cf0418f8-dd95-4514-ba3d-3cecca86caf9
Rogers, E
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Kummert, A
c665cd90-e430-47d3-9dfb-0ab3419c747f
Lam, J
56f6bc38-7d72-40f2-afde-20ff749c9dd4
Dabkowski, P
70e4f9ba-9370-45f9-b409-cccc563a2d8c
Galkowski, K
65b638be-b5a5-4e25-b1b8-e152c08a1cbb
Bachelier, O
cf0418f8-dd95-4514-ba3d-3cecca86caf9
Rogers, E
611b1de0-c505-472e-a03f-c5294c63bb72
Kummert, A
c665cd90-e430-47d3-9dfb-0ab3419c747f
Lam, J
56f6bc38-7d72-40f2-afde-20ff749c9dd4

Dabkowski, P, Galkowski, K, Bachelier, O, Rogers, E, Kummert, A and Lam, J (2013) Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes. Numerical Linear Algebra with Applications, 20, 220-233.

Record type: Article

Abstract

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model.

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Published date: 2013
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 272558
URI: http://eprints.soton.ac.uk/id/eprint/272558
PURE UUID: e7d014a6-27b9-49db-8e4d-818e394d3fbc
ORCID for E Rogers: ORCID iD orcid.org/0000-0003-0179-9398

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Date deposited: 11 Jul 2011 09:30
Last modified: 20 Jul 2019 01:23

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