Observer design for piecewise smooth and switched systems via contraction theory

The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of so-called Filippov systems (or variable structure systems) is based on the use of regularization, a procedure to make the vector field of interest differentiable before analyzing its properties. We show that by using this extension of contraction theory to nondifferentiable vector fields, it is possible to design observers for a large class of piecewise smooth systems using not only Euclidean norms, as also done in previous literature, but also non-Euclidean norms. This allows greater flexibility in the design and encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear) systems. The theoretical methodology is illustrated via a set of representative examples.Comment: Preprint accepted to IFAC World Congress 201

Contraction-based design of positive observers

We consider the problem of positive observer design for positive systems. We propose the design of a nonlinear positive observer based on the use of generalized polar coordinates in the positive orthant. The contraction properties of the estimation error are studied thanks to the Hilbert projective metric. The optimization problem of finding the observer gains that maximize the contraction rate is addressed, and the simple two-dimensional case is discussed in detail. Index Terms-Positive systems, non-linear Luenberger-type positive observers, contraction properties, Hilbert metric. © 2013 IEEE

Contraction-based design of positive observers

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