On mode reconstructability and reconstructability sets of piecewise linear systems

This paper focuses on the problem of mode reconstructability of piecewise linear multi-output systems for the case when a partition of the state space characterises the switching modes. The partition is assumed to be generated by an arbitrary number of parallel hyperplanes. The main results obtained are the necessary and sufficient conditions that the system must satisfy to be mode reconstructible on the whole state space. Furthermore, some other relevant results are also given, such as the characterisation of subsets of the state space where the system might be mode reconstructible whereas being mode unreconstructible anywhere else; and the conditions for mode discernibility/indiscernibility in some particular cases. The results can be summarised as a simple and easy criterion to verify the mode reconstructability property for the considered class of systems. For the sake of clarity, examples are included to illustrate the obtained results.