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A Lyapunov based analysis of convergence for the Super-Twisting algorithm for systems with uncertain control gain is presented. Through a Lyapunov function we have found the conditions over the matched perturbations and the uncertain control gain to preserve the properties of insensitivity and finite-time convergence to Sliding Modes of order two, that the Super-Twisting algorithm is able to achieve.
The aim of presented work consists in developing an active steering assistance system to avoid the lane departure of heavy vehicle. The controller is based on super twisting algorithm.
A new discrete time super-twisting-like second order sliding mode algorithm (DSTA) is proposed. The stability proof of the suggested scheme is analyzed in terms of the discrete Lyapunov approach and Linear Matrix Inequalities (LMI) theory. Using these two tools it is proved that, system state trajectory is ultimately bounded in finite time. The state estimation problem for a class of second order...
A sliding mode control is developed to solve the tracking control problem for an inertia wheel pendulum. The desired trajectory is centered at the upright position where the open-loop system becomes a non-minimum-phase system. As a first step towards the solution of the tracking control problem is the reference trajectory generation where we develop a reference model, based on the two-relay controller,...
The notion of strong observability is generalized for nonlinear systems. It allows to write the state of the system as a function of the measurable outputs and their time derivatives only, therefore allowing the construction of an unknown-input observer once such derivatives are estimated. It is shown that the output based control design problem for robust finite-time state stability for nonlinear...
An observer is designed for strongly detectable systems with unbounded unknown inputs. The design scheme is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as new states. Then, using a high-order sliding mode differentiator (HOSMD), a new output of the system is generated in order to fulfill the Hautus condition. Finally, the system...
In this paper we propose a whole family of quadratic-like strong Lyapunov functions for the Super Twisting algorithm. They show that all trajectories converge in finite time to the origin, and a formula to estimate the convergence time for the considered family of Lyapunov functions is proposed. A methodology to select the Lyapunov function, providing for better estimation of the convergence time,...
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