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Theses

Formulation générique de problèmes en analyse et commande robuste par les fonctions de Lyapunov dependant des paramètres

Dimitri Peaucelle 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The thesis addresses robustness problems in automatic control. Some property of a given system is said to be robust if it is invariant with respect to all admissible model uncertainties. Our aim is to give methods for finding a control law that improves and/or guarantees different robust properties. Linear time-invariant models are considered. The structured parametric uncertainties enter the model by linear fractional transformations while the uncertainty domain may be polytopic or dissipative. The robust properties studied in the thesis are robust stability, disturbance rejection (robust guaranteed cost) and transient response (pole location). First are given some analysis methods and then algorithms for control law synthesis are proposed. The theoretical tools employed are issued from the Lyapunov theory and from topological separation. Parameter dependent Lyapunov functions are considered in order to reduce the conservatism of the quadratic stability framework. This last framework is also described thoroughly for comparison in terms of conservatism and computational complexity. Most mathematical results are given in a unified formulation in order to describe their generality. All the results are based on linear matrix inequalities that can be solved efficiently with nowadays classical techniques. The theoretical results are illustrated by some examples.
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Dimitri Peaucelle. Formulation générique de problèmes en analyse et commande robuste par les fonctions de Lyapunov dependant des paramètres. Automatique / Robotique. Université Paul Sabatier - Toulouse III, 2000. Français. ⟨tel-00131516⟩

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