A sparse optimization approach to state observer design for switched linear systems

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, in contrast to the state of the art, it does not require an explicit prior estimation of the discrete state. The key idea of the method consists in minimizing a non-smooth ℓ2ℓ2-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 recent development in the literature of compressed sensing, the minimized cost functional has the ability to promote sparsity in a way that makes the knowledge of the discrete mode sequence unnecessary.