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Observer‐based control of linear complementarity systems
Author(s) -
Heemels W. P. M. H.,
Camlibel M. K.,
Schumacher J. M.,
Brogliato B.
Publication year - 2010
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.1626
Subject(s) - control theory (sociology) , observer (physics) , exponential stability , uniqueness , mathematics , state observer , passivity , separation principle , algebraic number , computer science , control (management) , nonlinear system , mathematical analysis , engineering , physics , quantum mechanics , artificial intelligence , electrical engineering
In this paper we present observer and output‐based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well‐posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer‐based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed‐loop system is well‐posed and globally exponentially stable. In order to show the well‐posedness of the closed loop, novel well‐posedness results for LCS based on low‐index properties are presented. Copyright © 2010 John Wiley & Sons, Ltd.