Parameter estimation of periodically switched linear systems

This study is concerned with parameter estimation of a special class of switched linear systems (SLSs), namely, periodically switched linear systems (PSLSs). General identification methods that do not explore switching sequence patterns may perform poorly in estimation accuracy and implementation efficiency. In this work, we first analyse input and output (I/O) data sequences and then establish the connection between the periodicity and I/O data sequence. This allows us to obtain an accurate estimation of the switching sequence period p₀. We prove that the correctness of data classification is almost surely guaranteed. In implementation, we propose two efficient strategies, namely, the reverse order search and finite data selection, to improve the computational efficiency. Moreover, we provide both offline and online methods to estimate p₀ and the parameters. The effectiveness of these methods are demonstrated in simulations.