Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Improved LMI Conditions for Unknown Input Observer Design of Discrete-time LPV Systems Matheus Senna de Oliveira* and Renan Lima Pereira 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. Keywords: Discrete-time LPV systems, linear matrix inequalities, poly-quadratic conditions, unknown input observers.
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INTRODUCTION
In recent years, linear parameter-varying (LPV) observer designs have been extensively studied in the control literature [1–4]. Much of this interest referred to the ability of represent nonlinear dynamics in terms of a family of linear time-invariant (LTI) systems using a scheduling strategy [5–7]. In early works, the observer was designed for each local subsystem, generating a set of LTI observers which are combined through some interpolation or scheduling procedure to compose the final observer law [8, 9]. Besides the intrinsic problem of state estimation, a crucial topic regarding LPV observers is the estimation of unknown inputs (UIs) [2, 4, 10]. In particular, the problem of estimating UIs has been playing an important role in practice since there are many situations where these exogenous signals are inaccessible [11] and may affect the state estimation performance [10, 12]. Among all potential approaches to estimate both states and unknown inputs satisfactorily, the one termed Unknown Input Observer (UIO) is undoubtedly a useful technique. Although the origins of the UIOs can be found in early 80s [14], several works regarding UIOs have been published in recent decades, including the design for nonlinear systems [15] and LPV systems [2,8,13,16] for both continuous- and discrete-time cases. For continuous-time case, a novel observer framework [2] using algebraic ma-
trix manipulation was presented. In this work only a proportional structure was addressed and existence conditions for convergence analysis in terms of Linear Matrix Inequalities (LMIs) were provided. However, a conservative quadratic conditions was used and the output matrix was considered time-invariant. Concerning discrete-time LPV systems, fewer works have considered existence conditions and synthesis procedures for such observers. Among these contributions, we may cite [8], which proposes a generalized dynamic
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