A new state observer for switched linear systems using a non-smooth optimization approach

A new continuous state observer is derived for discrete-time linear switched systems under the assumptions that neither the continuous state nor the discrete state are known. A specificity of the proposed observer is that, contrary to the state-of-art, it does not require an explicit estimation of the discrete state. The key idea of the method consists in minimizing a non-smooth l₂-norm-based weighted cost functional, constructed from the matrices of all the subsystems regardless of when each of them is active. In the light of some recent development in the literature of compressed sensing, the minimized cost functional has the ability to promote sparsity in a way that makes prior knowledge/estimation of the discrete mode sequence unnecessary.