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Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems

Matheus Senna de Oliveira* and Renan Lima Pereira
International Journal of Control, Automation, and Systems, vol. 18, no. 10, pp.2543-2551, 2020

Abstract : This paper presents a novel unknown input observer (UIO) design for discrete-time linear parametervarying (LPV) systems. One feature of the proposed approach is the ability of handling LPV systems with variation in both states and outputs matrices. The design problem has been formulated using a less conservative discrete-time stability condition which allows to obtain proportional UIO and proportional-integral UIO structures. Existence conditions for both structures are provided. These poly-quadratic conditions rely on the use of parameter-dependent Lyapunov functions defined in terms of Linear Matrix Inequalities. Furthermore, an extended formulation using the H∞ performance index is also derived. Finally, the effectiveness of the proposed design method is illustrated through numerical examples.

Keyword : Discrete-time LPV systems, linear matrix inequalities, poly-quadratic conditions, unknown input observers.

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