Asymptotic stability of nonlinear control systems described by difference equations with multiple delays.
Asymptotic stability of wave equations with memory and frictional boundary dampings
This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped. The result...
Asymptotical mean square stability of Cohen-Grossberg neural networks with random delay.
Asynchronous sampling-based leader- following consensus in second-order multi-agent systems
This paper studies the leader-following consensus problem of second-order multi-agent systems with directed topologies. By employing the asynchronous sampled-data protocols, sufficient conditions for leader-following consensus with both constant velocity leader and variable velocity leader are derived. Leader-following quasi-consensus can be achieved in multi-agent systems when all the agents sample the information asynchronously. Numerical simulations are provided to verify the theoretical results....
Attitude control of spacecraft
Backstepping based nonlinear adaptive control for the extended nonholonomic double integrator
In this paper a steering control algorithm for the Extended Nonholonomic Double Integrator is presented. An adaptive backstepping based controller is proposed which yields asymptotic stabilization and convergence of the closed loop system to the origin. This is achieved by transforming the original system into a new system which can be globally asymptotically stabilized. Once the new system is stabilized, the stability of the original system can be easily established. Stability of the closed loop...
Balanced reduction of linear periodic systems
For linear periodic discrete-time systems the analysis of the model error introduced by a truncation on the balanced minimal realization is performed, and a bound for the infinity norm of the model error is introduced. The results represent an extension to the periodic systems of the well known results on the balanced truncation for time-invariant systems. The general case of periodically time-varying state-space dimension has been considered.
Bilinear systems and chaos
Block bialternate sum with applications to computation of stability bounds
Boundary feedback stabilization of a hybrid PDE-ODE system.
Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach
In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...
Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach
In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...
Boundary stabilization of a coupled system of nondissipative Schrödinger equations.
Boundary stabilization of a linear elastodynamic systems with variable coefficients.
Boundary stabilization of Maxwell’s equations with space-time variable coefficients
We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks.
Boundary stabilization of Maxwell's equations with space-time variable coefficients
We consider the stabilization of Maxwell's equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard" identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. ...
Boundary stabilization of the linear elastodinamic system by a Lyapunov-type method.
We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.
Boundary stabilization of the Schrödinger equation in almost star-shaped domain
Bounded-input-bounded-state stabilization of switched processes and periodic asymptotic controllability
The main result of this paper is a sufficient condition for the existence of periodic switching signals which render asymptotically stable at the origin a linear switched process defined by a pair of real matrices. The interest of this result is motivated by the application to the problem of bounded-input-bounded-state (with respect to an external input) stabilization of linear switched processes.
Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons.