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Simple conditions for practical stability of positive fractional discrete-time linear systems

Mikołaj Busłowicz, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical...

Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty

A. Jafari Koshkouei, Alan S. I. Zinober (2000)

Kybernetika

This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics in the presence of unmatched uncertainty is also studied. When a certain sufficient condition on the gain feedback matrix of the discontinuous controller and the disturbance bound holds, then the disturbance does not affect the sliding system. The design of asymptotically stable sliding observers for linear multivariable systems is presented. A sliding...

Some remarks on matrix pencil completion problems

Jean-Jacques Loiseau, Petr Zagalak, Sabine Mondié (2004)

Kybernetika

The matrix pencil completion problem introduced in [J. J. Loiseau, S. Mondié, I. Zaballa, and P. Zagalak: Assigning the Kronecker invariants to a matrix pencil by row or column completions. Linear Algebra Appl. 278 (1998)] is reconsidered and the latest results achieved in that field are discussed.

Spatially-distributed coverage optimization and control with limited-range interactions

Jorge Cortés, Sonia Martínez, Francesco Bullo (2005)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect...

Spatially-distributed coverage optimization and control with limited-range interactions

Jorge Cortés, Sonia Martínez, Francesco Bullo (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius.
Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time.
These algorithms have convergence guarantees and are spatially distributed with...

Stabilité des systèmes à commutations du plan

Ugo Boscain, Grégoire Charlot, Mario Sigalotti (2009/2010)

Séminaire de théorie spectrale et géométrie

Soient X et Y deux champs de vecteurs lisses sur ℝ 2 globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où X et Y sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonome q ˙ ( t ) = u ( t ) X ( q ( t ) ) + ( 1 - u ( t ) ) Y ( q ( t ) ) où le contrôle u est une fonction mesurable arbitraire de [ 0 , + ∞ [ dans { 0 , 1 } . Les conditions données ne nécessitent aucune intégration ou construction d’une fonction de Lyapunov...

Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

Yang Liu, Rongjiang Yang, Jianquan Lu, Bo Wu, Xiushan Cai (2013)

International Journal of Applied Mathematics and Computer Science

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous...

Stability result for a thermoelastic Bresse system with delay term in the internal feedback

Lamine Bouzettouta, Sabah Baibeche, Manel Abdelli, Amar Guesmia (2023)

Mathematica Bohemica

The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first considered...

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