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LMI‐based second‐order sliding set design using reduced order of derivatives
Author(s) -
Márquez Raymundo,
Tapia Alán,
Bernal Miguel,
Fridman Leonid
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3295
Subject(s) - convergence (economics) , linear matrix inequality , set (abstract data type) , control theory (sociology) , regular polygon , mathematical optimization , convex optimization , order (exchange) , scheme (mathematics) , manifold (fluid mechanics) , computer science , derivative (finance) , mathematics , control (management) , engineering , artificial intelligence , financial economics , mechanical engineering , mathematical analysis , geometry , finance , economics , programming language , economic growth
Summary Sliding mode control design for systems with relative degree r requires a number r − 1 of time‐derivatives of the system output, which usually leads to deterioration of the whole scheme; if the highest‐order derivative is spared, a better precision is ensured. This paper proposes a control algorithm that guarantees reaching a second‐order sliding manifold using only r − 2 derivatives of the system output. This objective is achieved at the price of yielding finite‐time convergence while preserving the essential feature of insensitivity to matched disturbances. The results take full advantage of convex representations and linear matrix inequalities, whose formulation easily allows dealing with unmatched disturbances by convex optimization techniques already implemented in commercially available software. Simulation examples are included to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.