Observer design for piecewise smooth and switched systems via contraction theory
For control theorists, this provides a novel method to design observers for a broad class of nondifferentiable systems, offering more design flexibility than previous Euclidean-norm-based approaches.
The paper extends contraction theory to piecewise smooth and switched systems via regularization, enabling observer design with non-Euclidean norms for greater flexibility. The approach is demonstrated on representative examples.
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.