Observer Design for Lur'e Systems With Multivalued Mappings: A Passivity Approach

Bernard Brogliato 1 Maurice Heemels 2
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 TU/e - Eindhoven University of Technology [Eindhoven]
Abstract : This paper considers the design of state observers for Lur'e systems with multivalued mappings in the feedback path. In particular, we focus on maximal monotone mappings that that do not require any compactness and local boundedness properties and include various models for relays, friction characteristics and complementarity conditions. We propose two types of observers that are constructed by rendering a suitable operator passive in an appropriate sense. The well-posedness properties of the observer dynamics are carefully analyzed and the global asymptotic stability of the observation error is formally proven.
Keywords : Differential inclusion Lur'e systems maximal monotone mapping multivalued system normal cone observer passivity positive realness
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2009, 54 (8), pp.1996-2001. 〈10.1109/TAC.2009.2023968〉
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Bernard Brogliato, Maurice Heemels. Observer Design for Lur'e Systems With Multivalued Mappings: A Passivity Approach. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2009, 54 (8), pp.1996-2001. 〈10.1109/TAC.2009.2023968〉. 〈hal-00756302〉

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