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3 International Journal of Applied Mathematics and Computer Science

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H−/H∞ fault detection observer design for a polytopic LPV system using the relative degree

Zhou M., Rodrigues M., Shen Y., Theilliol D.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 1

83--95

This paper proposes an H−/H∞ fault detection observer method by using generalized output for a class of polytopic linear parameter-varying (LPV) systems. As the main contribution, with the aid of the relative degree of output, a new output vector is generated by gathering the original output and its time derivative, and it is feasible to consider H− actuator fault sensitivity in the entire frequency for the new system. In order to improve actuator and sensor fault sensitivity as well as guarantee robustness against disturbances, simultaneously, an H−/H∞ fault detection observer is designed for the new LPV polytopic system. Besides, the design conditions of the proposed observer are transformed into an optimization problem by solving a set of linear matrix inequalities (LMIs). Numerical simulations are provided to illustrate the effectiveness of the proposed method.

A multi-model approach to Saint-Venant equations: A stability study by LMIs

Dos Santos Martins V., Rodrigues M., Diagne M.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

539-550

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

Fault tolerant control design for polytopic LPV systems

Rodrigues M., Theilliol D., Aberkane S., Sauter D.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 1

27-37

This paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both faultfree and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.