This paper deals with the problem of state estimation for single-output linear systems. Under some structural properties of the system matrices it is possible to design a hybrid observer capable of estimating the state of the system exactly and in a finite time. Moreover, the proposed hybrid observer provides fixed-time convergence of the state estimation error, i.e. there exists a convergence time that is bounded and such a bound is independent of the initial estimation error. The robustness properties of the hybrid observer are analyzed for the linear system with unknown inputs, and the linear system with unknown inputs and parametric uncertainty. Some simulation results illustrate the effectiveness of the proposed hybrid observer.
Bibliographical noteFunding Information:
H. Ríos gratefully acknowledges the financial support from CONACYT 270504 . This work was supported in part by NSF grant ECCS-1508757, AFOSR grant FA9550-15-1-0155 . The material in this paper was partially presented at the 55th IEEE Conference on Decision and Control, December 12–14, 2016, Las Vegas, NV, USA. This paper was recommended for publication in revised form by Associate Editor Constantino M. Lagoa under the direction of Editor Richard Middleton.
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- Fixed-time convergence
- Hybrid observers
- Linear systems