Minimum energy control of fractional positive continuous-time linear systems with bounded inputs
Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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Tadeusz Kaczorek (2014)
International Journal of Applied Mathematics and Computer Science
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A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
Tadeusz Kaczorek (2013)
International Journal of Applied Mathematics and Computer Science
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De La Sen, M. (2011)
Abstract and Applied Analysis
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Łukasz Sajewski (2017)
International Journal of Applied Mathematics and Computer Science
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Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is...
Tadeusz Kaczorek (2013)
International Journal of Applied Mathematics and Computer Science
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Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.
De La Sen, M. (2011)
Fixed Point Theory and Applications [electronic only]
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Samir Ladaci, Abdelfatah Charef, Jean Jacques Loiseau (2009)
International Journal of Applied Mathematics and Computer Science
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This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed...
Tadeusz Kaczorek (2013)
International Journal of Applied Mathematics and Computer Science
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Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
Tricaud, Christophe, Chen, Yangquan (2010)
International Journal of Differential Equations
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Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)
International Journal of Applied Mathematics and Computer Science
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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...
Said Guermah, Said Djennoune, Maamar Bettayeb (2008)
International Journal of Applied Mathematics and Computer Science
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In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
Krishnan Balachandran, Shanmugam Divya (2014)
International Journal of Applied Mathematics and Computer Science
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Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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