Local Controllability of Quasilinear Integrodifferential Evolution Systems in Banach Spaces

Balachandran, K.; Park, J.Y.; Anandhi, E. R.

doi:10.1006/jmaa.2000.7388

Cited by 10 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar problem -a quasilinear delay integrodifferential equation has been considered e.g. in [2] (similar problems can be found also in [21,22] and many others chronologically subsequent papers).…”

Section: Introductionmentioning

confidence: 92%

See 1 more Smart Citation

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Djordjevic¹,

Konjik²,

Mitrović³

et al. 2021

Preprint

View full text Add to dashboard Cite

We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system, and then applying the Leray-Schauder fixed point theorem.We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so called global controllability).

show abstract

Section: Introductionmentioning

confidence: 92%

“…Nonlinear systems have been intensively considered recently and one can find various problems of this type in [2,4,14,20,27,28,29] and references therein. Let us briefly recall the related results from the field.…”

Section: Introductionmentioning

confidence: 99%

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Djordjevic¹,

Konjik²,

Mitrović³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Equation 9 represents a quasi-linear integrodifferential equation for which sufficient conditions for local controllability in Banach spaces have been established in [36]. Linear controllers for quasi-linear equations with bounded state-dependent nonlinear disturbances have been studied recently [37][38][39].…”

Section: Control Of the Oscillatormentioning

confidence: 99%

Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation

2008

View full text Add to dashboard Cite

We investigate the dynamics and control of a nonlinear oscillator that is described mathematically by a Variable Order Differential Equation (VODE). The dynamic problem in question arises from the dynamical analysis of a variable viscoelasticity oscillator. The dynamics of the model and the behavior of the variable order differintegrals are shown in variable phase space for different parameters. Two different controllers are developed for the VODEs under study in order to track an arbitrary reference function. A generalization of the van der Pol equation using the VODE formulation is analyzed under the light of the methods introduced in this work.Keywords Fractional derivatives and integrals · Variable order differential equations · Control of nonlinear oscillators · van der Pol equation

show abstract

“…Further, the quasi-linear integro-differential equations have occurred during the study of the nonlinear behavior of elastic strings and other areas of physics. Many interesting results on various forms of systems, including fractional-order, quasi-linear, integro-differential and non-local systems, are found in [11][12][13][14][15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

Mathiyalagan

Zeng

Yavuz

2022

Axioms

View full text Add to dashboard Cite

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.

show abstract

Local Controllability of Quasilinear Integrodifferential Evolution Systems in Banach Spaces

Abstract: Sufficient conditions for local controllability of quasilinear integrodifferential systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

Cited by 10 publications

References 24 publications

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs

Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

Contact Info

Product

Resources

About