Exponential stability of a nonlinear distributed parameter system.
Exponential stability of two coupled second-order evolution equations.
Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics
Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These...
External stabilization of discontinuous systems and nonsmooth control Lyapunov-like functions.
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
Fault tolerant control of switched nonlinear systems with time delay under asynchronous switching
This paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is utilized for stability analysis and controller design. Then the proposed approach is extended to take into...
Generalized immersion and nonlinear robust output regulation problem
The problem of output regulation of the system affected by unknown constant parameters is considered here. Under certain assumptions, such a problem is known to be solvable using error feedback via the so-called immersion to an observable linear system with outputs. Nevertheless, for many interesting cases this kind of finite dimensional immersion is difficult or even impossible to find. In order to achieve constructive procedures for wider classes, this paper investigates a more general type of...
Global asymptotic stabilisation of an active mass damper for a flexible beam
In this paper, a finite dimensional approximated model of a mechanical system constituted by a vertical heavy flexible beam with lumped masses placed along the beam and a mobile mass located at the tip, is proposed; such a model is parametric in the approximation order, so that a prescribed accuracy in the representation of the actual system can be easily obtained with the proposed model. The system itself can be understood as a simple representation of a building subject to transverse vibrations,...
Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method.
Global finite-time observers for a class of nonlinear systems
Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.
Global output feedback stabilization for nonlinear fractional order time delay systems
This paper investigates the problem of global stabilization by state and output-feedback for a family of for nonlinear Riemann-Liouville and Caputo fractional order time delay systems written in triangular form satisfying linear growth conditions. By constructing a appropriate Lyapunov-Krasovskii functional, global asymptotic stability of the closed-loop systems is achieved. Moreover, sufficient conditions for the stability, for the particular class of fractional order time-delay system are obtained....
Global phase synchronization for a class of dynamical complex networks with time-varying coupling delays.
Hierarchical sliding mode control for a class of SIMO under-actuated systems
Independence of asymptotic stability of positive 2D linear systems with delays of their delays
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Linear approach for synchronous state stability in fully connected PLL networks.
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained...
Mathematical model and optimal control of flow induced vibration of pipelines
In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.