Robust $H_{\infty}$ Interval Observer for Linear Systems With a Controllable Convergence Rate: A Parametric Method

In this paper, the design method of a robust interval observer for linear systems with time-varying disturbances is proposed. First, the H
_∞
gain performance is established by constructing the transfer function from disturbances to error dynamic systems of the interval observers. Second, the design problem about a robust interval observer, equivalent to the eigenstructure assignment of the observer error systems under the above form and the idea of the eigenstructure decomposition, is solved. Finally, in view of this situation where there does not exist an observation gain ensuring the cooperativity of the error systems, a novel parametric approach to design an interval observer with a controlled convergence rate and the robustness with respect to disturbances is proposed by a linear transformation and the solutions to a type of generalized Sylvester equations. Besides, the correctness and efficiency of the obtained results are illustrated by numerical examples and an actual physical system about the longitudinal motion of a Charlie Aircraft.