Multirate Symbolic Models for Incrementally Stable Switched Systems

International audienceMethods for computing approximately bisimilar symbolic models for incrementally stable switched systems are usually based on discretization of time and space, where the value of time and space sampling parameters must be carefully chosen in order to achieve a desired precision. This often results in symbolic models that have a very large number of transitions, especially when the time sampling, and thus the space sampling parameters are small. In this paper, we present an approach to the computation of symbolic models for switched systems using multirate time sampling, where the period of symbolic transitions is a multiple of the control (i.e. switching) period. We show that multirate symbolic models are approximately bisimilar to the original incrementally stable switched system. The main contribution of the paper is the explicit determination of the optimal sampling ratio between transition and control periods, which minimizes the number of transitions in the symbolic model. Interestingly, this optimal sampling ratio is mainly determined by the state space dimension and the number of modes of the switched system. Finally, an illustration of the proposed approach is shown for the boost DC-DC converter, which shows the benefit of multirate symbolic models