System identification for switched linear systems from input output data has received substantial attention in recent years. There is a growing interest for techniques that pose the identification problem as a sparse optimisation problem. At the same time a vast amount of research is dedicated to improving SAT solvers which as a result become faster every year. In this work a novel identification method for Switched AutoRegressive eXogenous (SARX) systems
and PieceWise AutoRegressive eXogenous (PWARX) systems is proposed that combines sparse optimisation with a SAT solver. The presented method aims to minimise the number of submodels needed to fit the data, while facilitating a prescribed minimum dwell time between switches. The procedure for the identification of switched ARX models is composed of two steps. The First phase determines the switching times in an iterative process aided by a SAT solver. Second, the model parameters and the switching sequence are estimated by
optimising the sparsity of a sequence. The identification procedure for PWARX models operates similarly although it incorporates the knowledge that switches depend on the regressor. An extension to these methods that makes the identification of large datasets tractable is also put forward. The proposed algorithm is evaluated on synthetic systems from the literature and shows promising results. Finally, the proposed algorithm is applied to an experimental benchmark dataset for a nonlinear system. All the algorithms proposed in this thesis project are implemented in the form of a toolbox that is made publicly available.