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Archives of Control Sciences
EN The realization problem for positive fractional continuous-time linear systems is addressed. Sufficient conditions for the existence of positive realizations for continuous-time linear systems are established. Procedures for computation of positive fractional realizations for SISO and MIMO continuou[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
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Archives of Control Sciences
2019 Vol. 29, No. 3 549--567
EN The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2019 Vol. 67, nr 6 989--993
EN The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN The stability problem of continuous-time linear systems described by the state equation consisting of n subsystems with different fractional orders of derivatives of the state variables has been considered. The methods for asymptotic stability checking have been given. The method proposed in the gen[...]
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Control and Cybernetics
EN A new class of singular fractional linear discretetime systems is introduced. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional linear systems is derived. The considerations are illustrated by numerical examples.
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems with a diagonal state matrix are addressed. Standard and positive systems are considered. Simple necessary and sufficient analytic conditions for practical stability and for asymptoti[...]
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Journal of Automation Mobile Robotics and Intelligent Systems
EN A dynamical system described by homogeneous equation is called pointwise complete if every final state can be reached by suitable choice of the initial state. The system which is not pointwise complete is called pointwise degenerated. Definitions and necessary and sufficient conditions for the point[...]
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Journal of Automation Mobile Robotics and Intelligent Systems
EN The paper considers the stability problem of linear time-invariant continuous-time systems of fractional commensurate order. It is shown that the system is stable if and only if plot of rational function of fractional order, called as the generalised modified Mikhailov plot, and does not encircle th[...]
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Journal of Automation Mobile Robotics and Intelligent Systems
EN In the paper the positive fractional discrete-time linear systems with delay described by the state equations are considered. The solution to the state equations is derived using the Z transform. Necessary and sufficient conditions are established for the positivity, reachability and controllability[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2013 Vol. 61, nr 4 779--786
EN In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state [...]
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Archives of Control Sciences
EN Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.
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Archives of Control Sciences
2015 Vol. 25, no. 4 491--496
EN The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are[...]
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Archives of Control Sciences
2017 Vol. 27, no. 1 119--128
EN The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical examp[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with s[...]
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Journal of Automation Mobile Robotics and Intelligent Systems
EN A new class of fractional linear continuous-time linear systems described by the state equation is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of the fractional sy[...]
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Control and Cybernetics
EN The problem of stabilization of fractional positive linear continuous-time linear systems with delays by state-feedbacks is addressed. The gain matrix of the state feedback is chosen so that the zeros of the closed-loop polynomial are located in a sector of the left half of complex plane. Necessary [...]
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Journal of Automation Mobile Robotics and Intelligent Systems
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2013 Vol. 61, nr 2 349--352
EN The asymptotic stability of positive fractional switched continuous-time linear systems for any switching is addressed. Simple sufficient conditions for the asymptotic stability of the positive fractional systems are established. It is shown that the positive fractional switched systems are asymptot[...]
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Archives of Control Sciences
EN The positive linear fractional discrete-time Lyapunov systems are introduced. The necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual [...]
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