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Backstepping based nonlinear adaptive control for the extended nonholonomic double integrator

Waseem Abbasi, Fazal ur Rehman, Ibrahim Shah (2017)

Kybernetika

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

Sauro Longhi, Giuseppe Orlando (1999)

Kybernetika

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.

Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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 Maxwell’s equations with space-time variable coefficients

Serge Nicaise, Cristina Pignotti (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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

Serge Nicaise, Cristina Pignotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Rabah Bey, Amar Heminna, Jean-Pierre Lohéac (2003)

Revista Matemática Complutense

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.

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