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Asymptotic stability of sampled-data piecewise affine slab systems


Asymptotic stability of sampled-data piecewise affine slab systems

Moarref, Miad and Rodrigues, Luis (2012) Asymptotic stability of sampled-data piecewise affine slab systems. Automatica, 48 (11). pp. 2874-2881. ISSN 00051098

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rodrigues_moarref_asymptotic_2012.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1016/j.automatica.2012.08.028


This paper addresses stability analysis of closed-loop sampled-datapiecewiseaffine (PWA) slabsystems. In particular, we study the case in which a PWA plant is in feedback with a discrete-time emulation of a PWA controller. We consider the sampled-datasystem as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov–Krasovskii functional (LKF) for studying PWA systems with time delays that is less conservative when compared to previously suggested alternatives. Second, based on the new LKF, sufficient conditions are provided for asymptoticstability of sampled-data PWA slabsystems to the origin. These conditions become Linear Matrix Inequalities (LMIs) in the case of a piecewise linear (PWL) controller. Finally, we present an algorithm for finding a lower bound on the maximum delay that preserves asymptoticstability. Therefore, the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptoticstability of the sampleddatasystem. The new results are successfully applied to a unicycle example.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Authors:Moarref, Miad and Rodrigues, Luis
Journal or Publication:Automatica
Digital Object Identifier (DOI):10.1016/j.automatica.2012.08.028
ID Code:974924
Deposited On:30 Oct 2012 16:40
Last Modified:18 Jan 2018 17:39
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