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Uniformly convergent sliding mode‐based observation for switched linear systems
Author(s) -
Mincarelli D.,
Pisano A.,
Floquet T.,
Usai E.
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.3366
Subject(s) - convergence (economics) , mathematical proof , control theory (sociology) , observer (physics) , mathematics , state (computer science) , projection (relational algebra) , residual , lyapunov function , state observer , discrete time and continuous time , computer science , algorithm , nonlinear system , geometry , artificial intelligence , statistics , physics , control (management) , quantum mechanics , economics , economic growth
Summary The problem of designing an observer capable of reconstructing the continuous and discrete states for a class of switched linear systems is addressed. A stack of dynamical observers based on the super twisting algorithm with finite and uniform‐in‐the‐initial‐condition convergence is considered, which provides an estimate of the continuous state and, at the same time, produces residual signals suitable for reconstructing the discrete state. An appropriate ‘projection’ of the residuals is suggested, which allows to speed up the reconstruction of the discrete state. Formal ‘distinguishability’ conditions guaranteeing that the discrete state can be uniquely reconstructed are derived. Lyapunov‐based proofs of convergence, and numerical simulations, support the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.