Journal Article10.1108/03684920910976826
Fractional positive linear systems
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TL;DR: A new class of fractional positive continuous‐time and discrete‐time linear systems with requirements for the internal and external positivity and of the reachability and controllability to zero of the fractional systems is introduced.
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Abstract: Definition 1.3 of (backward) fractional difference of α-order will be extended to two-dimensional (shortly 2D) discrete function x ij .
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Citations
Positive Linear Systems Consisting of $n$ Subsystems With Different Fractional Orders
TL;DR: It is shown that the linear electrical circuits composed of resistors, supercondensators, coils, and voltage (current) sources are positive systems with different fractional orders.
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Comparison of h -Difference Fractional Operators
Dorota Mozyrska,Ewa Girejko,Małgorzata Wyrwas +2 more
- 01 Jan 2013
TL;DR: The formula for fundamental matrix of solutions for linear systems of h-difference fractional equations with Grunwald-Letnikov type operator while the one with Caputo type or Riemann-Liouville type is well known is introduced.
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Positive stable realizations with system Metzler matrices
TL;DR: In this paper, conditions for the existence of positive stable realizatio ns with system Metzler matrices for linear continuous-time systems are established and a procedure for finding a positive stable realization with system metzler matrix based on similarity transformation of proper transfer matrices is proposed and demonstrated on numerical examples.
39
Local controllability of nonlinear discrete-time fractional order systems
Dorota Mozyrska,Ewa Pawluszewicz +1 more
TL;DR: In this article, the controllability problem of a nonlinear fractional order discrete-time system is solved using the Riemann-Liouville, Caputo and Grünwald-Letnikov fractional-order difference operators.
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Stability of state-space models of linear continuous-time fractional order systems
TL;DR: In this paper, the stability problem of linear time-invariant continuous-time systems of fractional order, standard and positive, described by the state space model, is considered.
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Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
Igor Podlubny,B. Nemcovej +1 more
TL;DR: In this paper, a solution to the more than 300-year old problem of geometric and physical interpretation of fractional integration and dieren tiation is suggested for the Riemann-Liouville fractional Integration and Dieren Tiation, the Caputo fractional dierentiation, and the Riesz potential.
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Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation
TL;DR: In this paper, a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems is presented, and a simple numerical example of linear state estimation is presented.