Abstract
In this paper, the design method of a robust interval observer for linear systems with time-varying disturbances is proposed. First, the $H_{\infty }$ -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.
Highlights
Aiming at this widespread problem where some physical states are quite difficult to be directly measured in the actual control engineering, the research on the state reconstruction problem has been intensively concerned by numerous researchers
ROBUST INTERVAL OBSERVER DESIGN According to Definition 3, there exists the following right coprime factorization (RCF)
Based on the solution to a type of the Sylvester equations, the conditions of designing a robust interval observer are transformed into the parametric forms, related to eigenvalues and eigenvectors matrix V, l = 1, 2, · · ·, n, i = 1, 2, · · ·, β0, j = 1, 2, · · ·, n
Summary
Aiming at this widespread problem where some physical states are quite difficult to be directly measured in the actual control engineering, the research on the state reconstruction problem has been intensively concerned by numerous researchers. A time-invariant change of coordinates was applied to design a full-order interval observer for nonlinear systems in [19]. The design thought of a reduced-order interval observer was firstly proposed for the time-delay systems by Efimov et al [20]. In view of the limitations of the simple linear time-invariant model in describing dynamics, the systems with the additional characteristics were deeply considered in the development process of the interval observers, such as time-delay [22], time-varying [23], [24], switching [25]–[27] or fuzzy [28].
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