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This paper deals with the stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an H ∞ criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.

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A new approach is presented for sensor fault detection reconstruction and state estimation. The system considered is linear polytopic parameter-vary ing (LPV) system. The main idea is the design of a novel robust adaptive observer based on and polyquadratic formulation with a new set of relaxation. Sufficient conditions are given by a set of Linear Matrix Inequalities (LMI) in order to guarantee the stability of the system and the asymptotic convergence of the fault error. A simulation example has been studied to illustrate the proposed methods by detecting constant and variable sensor fault.