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We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.

In this paper, incremental exponential asymptotic stability of a class of switched Carathéodory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients between these norms. This model is rather general and includes the case of staircase switching signals as a special case. Sufficient conditions are derived for incremental stability allowing for the system to be incrementally exponentially asymptotically stable even if some of its modes are unstable in some time periods. Numerical examples on switched linear systems with periodic switching and on the synchronization of switched networks of nonlinear systems are used to illustrate the theoretical results.

This paper is concerned with the design and implementation of a simple but effective switching control strategy to regulate the dynamics of synthetic gene networks. The testbed circuit is IRMA, a recently developed network in S. Cerevisiae which is proposed as a suitable benchmark problem for control design. The proof-of-concept of an implementation of the control strategy in vivo is presented which is based on the use of microfluidics devices and fluorescence microscopy. Preliminary experimental results are given showing the good matching between the model predictions and the experimental observations. (C) 2011 Elsevier Ltd. All rights reserved.