Data-based control design methods most often consist of iterative adjustment of the controller's parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization - no process model is used. The convergence to the global minimum of the performance criterion depends on the initial controller parameters and on the step size of each iteration. This paper discusses these issues and provides a method for choosing the step size to ensure convergence to the global minimum utilizing the lowest possible number of iterations.

This paper addresses the problem of tracking constant references for linear systems subject to control saturation. Considering an unitary output feedback loop, containing an integral action, conditions in LMI form are proposed to compute a state feedback and an integrator anti-windup gain. These conditions ensure that the trajectories of the closed-loop system are bounded in an invariant ellipsoidal set, provided that the initial conditions are taken in this set and the references and the disturbances belong to a certain admissible set. Based on these conditions, optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed.

In this work, a systematic methodology to design dynamic output feedback controllers, for linear control systems presenting both actuator and sensor saturations, is proposed. A theoretical condition that ensures that the trajectories of the closed-loop system are bounded for L2 disturbances, while ensuring internal global asymptotic stability is stated. From this theoretical condition an LMI-based optimization problem to compute the controller aiming at minimizing the induced L2 gain between the disturbance and the regulated output is proposed.

The prEservation of Onsager symmetry for the effective dielectric tensor is discussed for a homogeneous Plasma immersed in a inhomogeneous magnetic ?eld, using the unperturbed orbits correct up to order $k\_B$, which is the scalelength of the field inhomogeneity. General features of the calculation of the components of the tensor are discussed and detailed calculations are developed for the $zz$ component, which is shown to satisfy the conditions for Onsager symmetry, in agreement with prEvious results obtained using less prEcise exprEssions for the unperturbed orbits.