Design of parametric unknown input observers in linear time-invariant systems

A parametric design problem of the unknown input observers in the linear time-invariant systems is investigated. The aim is to design the parametric expression of the state observers that can estimate the state of the linear time-invariant systems with the unknown input disturbances. Based on the parametric solutions of a Sylvester matrix equation, the parametric expressions of all the gain matrices in the unknown input observers are put forward and the free parameters included in the parametric observers can offer all the degrees of design freedom in designing control system. Finally, a simulation example shows the proposed parametric design method of the unknown input observers in the linear time-invariant system is feasible.

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