Control synthesis for polynomial discrete-time systems under input constraints via delayed-state Lyapunov functions

This paper presents a discrete-time control design methodology for input-saturating systems using a Lyapunov function with dependence on present and past states. The approach is used to bypass the usual difficulty with full polynomial Lyapunov functions of expressing the problem in a convex way. Als...

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Bibliographic Details
Published in:International journal of systems science Vol. 47; no. 5; pp. 1176 - 1184
Main Authors: Pitarch, J.L., Sala, A., Lauber, J., Guerra, T.M.
Format: Journal Article
Language:English
Published: Taylor & Francis 03.04.2016
Subjects:
Automatic
Computer programs
control design
Control systems
Controllers
convex optimisation
delayed Lyapunov function
Design engineering
discrete time
Engineering Sciences
Lyapunov functions
polynomial systems
Polynomials
Programming
Saturation
SOS approach
stabilisation
ISSN:0020-7721, 1464-5319
Online Access:Get full text
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Summary:This paper presents a discrete-time control design methodology for input-saturating systems using a Lyapunov function with dependence on present and past states. The approach is used to bypass the usual difficulty with full polynomial Lyapunov functions of expressing the problem in a convex way. Also polynomial controllers are allowed to depend on both present and past states. Furthermore, by considering saturation limits on the control action, the information about the relationship between the present and past states is introduced via Positivstellensatz multipliers. Sum-of-squares techniques and available semi-definite programming (SDP) software are used in order to find the controller.
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ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2014.915357