scholarly journals Robust Stabilization Approach and Performance via Static Output Feedback for a Class of Nonlinear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Neila Bedioui ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Robust Stabilization ◽  
Nonlinear Function ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Lmi Optimization ◽  
And Performance ◽  
The Stability ◽  
Static Output

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 criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.

scholarly journals LMI Formulation for Static Output Feedback Design of Discrete-Time Switched Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Selma Ben Attia ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Small Degree ◽  
Switched System ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Feedback Design ◽  
And Performance ◽  
Static Output

This paper concerns static output feedback design of discrete-time linear switched system using switched Lyapunov functions (SLFs). A new characterization of stability for the switched system under arbitrary switching is first given together with -performance evaluation. The various conditions are given through a family of LMIs (Linear Matrix Inequalities) parameterized by a scalar variable which offers an additional degree of freedom, enabling, at the expense of a relatively small degree of complexity in the numerical treatment (one line search), to provide better results compared to previous one. The control is defined as a switched static output feedback which guarantees stability and -performance for the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed conditions.

An Application of QSR-Dissipativity to the Problem of Static Output Feedback Robust Stabilization of Nonlinear Systems

2020 ◽  
Author(s):  
Diego De S. Madeira ◽  
Valessa V. Viana
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Domain Of Attraction ◽  
Control Synthesis ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Static Feedback ◽  
Static Output

In this work we deal with the asymptotic stabilization problem of polynomial (and rational) input-affine systems subject to parametric uncertainties. The problem of linear static output feedback (SOF) control synthesis is handled, having as a prerequisite a differential algebraic representation (DAR) of the plant. Using the property of strict QSR-dissipativity, theFinsler's Lemma and the notion of linear annihilators we introduce a new dissipativity-based strategy for robust stabilization which determines a static feedback gain by solving a simple linear semidenite program on a polytope. At the same time, an estimate of the closed-loop domain of attraction is given in terms of an ellipsoidal set. The novelty of the proposed approach consists in this combination of dissipativity theory and powerful semidenite programming(SDP) tools allowing for a simple solution of the challenging problem of static output feedback design for nonlinear systems. A numerical example allows the reader to verify the applicability of the proposed technique.

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