Constrained controllability of semilinear systems with delays

Klamka, Jerzy

doi:10.1007/s11071-008-9389-4

Cited by 82 publications

(46 citation statements)

References 8 publications

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“…Constrained controllability of integer order systems with delays was discussed, among others, by Sikora (2003;2005), Klamka (2008;2009), or Sikora and Klamka (2012). Works on controllability of linear fractional systems with bounded inputs include those by Kaczorek (2014a;2014b) for fractional positive discrete-time linear systems and fractional positive continuous-time…”

Section: Introductionmentioning

confidence: 99%

Controllability criteria for time–delay fractional systems with a retarded state

Sikora

2016

International Journal of Applied Mathematics and Computer Science

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The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.

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Section: Introductionmentioning

confidence: 99%

Controllability criteria for time–delay fractional systems with a retarded state

Sikora

2016

International Journal of Applied Mathematics and Computer Science

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“…The finite-dimensional dynamical control systems depicted in semilinear ordinary differential state equations [4]. The multiple point time-variable delays in control are carried out.…”

Section: Introductionmentioning

confidence: 99%

Existence of Mild Solutions for Fractional Neutral Functional Differential Equations

2016

IJSR

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Abstract:In several research works, controllability is one of the major concepts in mathematical control theory, which plays an important role in control systems. The controllability of nonlinear systems provided by evolution equations and qualitative theory of fractional differential equations has been developed. In this paper, we consider the initial value problems of fractional neutral functional differential equations. By applying fixed-point theorem, fractional calculus and controllability theory, a new set of acceptable conditions for approximate controllability of semi linear fractional differential equations are formulated and verified. Finally approximate controllability of semi linear fractional control differential systems is implied under the assumptions that the corresponding linear system is approximately controllable.

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“…The controllability of infinite dimensional systems has been studied in [9,10]. Further investigation has addressed the problem for stochastic [11,12,13,14], delayed [15,16], fractional [17,18,19] and switched [20,21,22,23] systems.…”

Section: Introductionmentioning

confidence: 99%

A practical test for assessing the reachability of discrete-time Takagi–Sugeno fuzzy systems

Witczak

Rotondo

Puig

et al. 2015

Journal of the Franklin Institute

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This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the reachability analysis can be performed efficiently using the proposed approach.

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Constrained controllability of semilinear systems with delays

Cited by 82 publications

References 8 publications

Controllability criteria for time–delay fractional systems with a retarded state

Controllability criteria for time–delay fractional systems with a retarded state

Existence of Mild Solutions for Fractional Neutral Functional Differential Equations

A practical test for assessing the reachability of discrete-time Takagi–Sugeno fuzzy systems

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