## A sparse optimization approach to state observer design for switched linear systems.(English)Zbl 1259.93028

Summary: 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 $$\ell _{2}$$-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.

### MSC:

 93B07 Observability 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93C05 Linear systems in control theory
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