Stability of stochastic functional differential equations and the W-transform.
Stability results for switched linear systems with constant discrete delays.
Stabilizability and disturbance rejection with state-derivative feedback.
Stabilizability of a class of nonlinear systems using hybrid controllers.
Stabilization criteria for continuous linear time-invariant systems with constant lags.
Stabilization of a 1-D tank modeled by the shallow water equations
We consider a tank containing a fluid. The tank is subjected to a one-dimensional horizontal move and the motion of the fluid is described by the shallow water equations. By means of a Lyapunov approach, we deduce control laws to stabilize the fluid's state and the tank's position. Although global asymptotic stability is yet to be proved, we numerically simulate the system and observe the stabilization for different control situations.
Stabilization of a coupled multidimensional system.
We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.
Stabilization of a hybrid system: An overhead crane with beam model.
Stabilization of a hybrid system with a nonlinear nonmonotone feedback
Stabilization of a hybrid system with a nonlinear nonmonotone feedback
For a hybrid system composed of a cable with masses at both ends, we prove the existence of solutions for a class of nonlinear and nonmonotone feedback laws by means of a priori estimates. Assuming some local monotonicity, strong stabilization is obtained thanks to some Riemann's invariants technique and La Salle's principle.
Stabilization of bilinear systems by a linear feedback control
Stabilization of discrete-time control systems with multiple state delays.
Stabilization of fractional exponential systems including delays
This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular...
Stabilization of fractional positive continuous-time linear systems with delays in sectors of left half complex plane by state-feedbacks
Stabilization of heterogeneous Maxwell's equations by linear or nonlinear boundary feedbacks.
Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces.
Stabilization of linear sampled-data systems by a time-delay feedback control.
Stabilization of nonlinear discrete-time systems via a digital communication channel.
Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback
In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this...
Stabilization of nonlinear stochastic systems without unforced dynamics via time-varying feedback
In this paper we give sufficient conditions under which a nonlinear stochastic differential system without unforced dynamics is globally asymptotically stabilizable in probability via time-varying smooth feedback laws. The technique developed to design explicitly the time-varying stabilizers is based on the stochastic Lyapunov technique combined with the strategy used to construct bounded smooth stabilizing feedback laws for passive nonlinear stochastic differential systems. The interest of this...