Section: New Results

Sliding Mode Control And Estimation

• The paper [22] addresses the problem of oscillatory failure case detection in the electrical flight control system of a generic commercial airplane. A non-homogeneous differentiator is first used to provide accurate derivatives in noisy environment and fast convergence time. In this study case, fault detection is addressed in the unknown input estimation issue for fault reconstruction with the same evaluation techniques currently employed in Airbus A380 airplanes. Performance and robustness of the developed monitoring strategy are assessed using a high-fidelity Airbus benchmark and a parametric test campaign for the flight scenarios defined in the EU-FP7 ADDSAFE project.

• A new sliding mode control approach is introduced in [26] with the dedicated mathematical tools. A time-delay modification/approximation of sign function is proposed in [57] , and it is shown that by substituting this new "sign " realization in the conventional sliding mode algorithms the main advantages of the sliding mode tools are preserved (like rejection of matched disturbances and hyper-exponential convergence), while the chattering is reduced.

• The article [34] proposes a convex optimization approach for the design of relay feedback controllers. The case of linear systems is studied in the presence of matched perturbations. The system input is a generalized relay that may take values in a finite set of constant vectors. A simple design method is proposed using Linear Matrix Inequalities (LMIs).

• In the note [53] we study the effect of an implicit Euler time-discretization method on the stability of the discretization of a globally fixed-time stable, scalar differential inclusion representing a simple nonlinear system with a set-valued signum controller. The controller nonlinearity is a cubic term and it is shown that the fully-implicit method preserves the global Lyapunov stability property of the continuous-time system, contrarily the explicit discretization which does not. It allows to obtain finite-time convergence to the origin when the plant is undisturbed, while the cubic term provides the hyper-exponential convergence rate.

• The problem of finite-time stabilization of multi-input linear system by means of sliding mode relay feedback is considered in [68] . A new control design procedure, which combines convex embedding technique with implicit Lyapunov function method, is developed. The issues of practical implementation of the obtained implicit relay feedback are discussed. Theoretical result is supported by numerical simulation.