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Stability and stabilization of one class of three time-scale systems with delays

Valery Y. Glizer (2022)

Kybernetika

A singularly perturbed linear time-invariant time delay controlled system is considered. The singular perturbations are subject to the presence of two small positive multipliers for some of the derivatives in the system. These multipliers (the parameters of singular perturbations) are of different orders of the smallness. The delay in the slow state variable is non-small (of order of 1 ). The delays in the fast state variables are proportional to the corresponding parameters of singular perturbations....

Stability of a class of adaptive nonlinear systems

Andrzej Dzielinski (2005)

International Journal of Applied Mathematics and Computer Science

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear...

Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case

Tomasz Zubowicz, Mietek A. Brdyś (2013)

International Journal of Applied Mathematics and Computer Science

This paper addresses the problem of model-based global stability analysis of discrete-time Takagi-Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov function, which may in some cases be too conservative, and a fuzzy Lyapunov...

Stabilization of a 1-D tank modeled by the shallow water equations

Christophe Prieur, Jonathan de Halleux (2002)

Journées équations aux dérivées partielles

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.

Serge Nicaise, Abdoulaye Sène (2006)

Revista Matemática Complutense

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 with a nonlinear nonmonotone feedback

Eduard FEIREISL, Geoffrey O'DOWD (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 fractional exponential systems including delays

Catherine Bonnet, Jonathan R. Partington (2001)

Kybernetika

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...

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