This PhD thesis focuses on the synthesis of a novel control architecture for Switched Affine Systems (SAS) subject to exogenous disturbances. Building upon the established expertise of the supervisors in hybrid/switched systems and state-space representations of power converters [9, 19, 8], this thesis addresses the fundamental challenge of stabilizing SAS when the equilibrium point is uncertain due to the inevitable effect of unmeasured perturbations.The project hinges upon a novel nonlinear control structure based on four ingredients: a switched observer for simultaneous state and disturbance reconstruction, a nonlinear observer for the estimation of the unknown equilibrium to be stabilized, integrated with an optimization mechanism allowing for efficient online gradient-based selection of an optimal operating point and a switched stabilizer. The core theoretical innovation is threefold: (i) managing the inherent non-smoothness of cost functions (e.g., L1-norm penalties) through sub-gradients and differential inclusions (ii) exploring the use of modern nonquadratic Lyapunov certificates of asymptotic stability of the error dynamics leveraging recent advances in nonlinear integral action [1] (iii) using modern hybrid dynamical systems tools and reduction theory [16] to establish desirable stability and optimality properties of the interconnected scheme. This work aims to transcend standard quadratic constraints by to ensure global asymptotic stability in complex switching environments. Contacts : Luca Zaccarian lzaccari@laas.fr and Yassine Ariba yariba@laas.fr