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On the Observablity of Linear Nonstationary Fractional Systems
2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR), 2018The paper is deals with a problem of observability of time variant linear fractional systems. We present definition of the estimation of initial conditions from the output of the system. By solutions representation we establish necessary and sufficient conditions for the defined observability. The considerations are illustrated by examples.
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Linear fractional representations of uncertain systems
Autom., 1997A systematic procedure to find low-order linear fractional representations of systems with parametric uncertainty has been developed. The multidimensional realization theory for MIMO systems has been employed.
Juan C. Cockburn, Blaise G. Morton
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On the Fractional Linear Scale Invariant Systems
IEEE Transactions on Signal Processing, 2010The linear scale invariant systems are introduced for both integer and fractional orders. They are defined by the generalized Euler-Cauchy differential equation. The quantum fractional derivatives are suitable for dealing with this kind of systems, allowing us to define impulse response and transfer function with the help of the Mellin transform. It is
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Fractional discrete-time linear systems
1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002In this paper, the class of discrete linear systems is enlarged with the inclusion of the discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how to compute the impulse response and transfer function.
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Fractional representations of linear systems
Systems & Control Letters, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lomadze, V., Zerz, E.
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Linear fractional shift invariant (LFSI) systems
Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings., 2003In this paper, we formulate continuous time linear fractional shift invariant (LFSI) systems that generalize the well-known linear time invariant (LTI) systems by means of an angle parameter /spl phi/. LTI systems are obtained as a special case of LFSI systems for /spl phi/ = 0. LFSI systems belong to the large class of time-varying systems.
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Note on controllability of linear fractional dynamical systems
Journal of Control and Decision, 2016In this article, we obtain the solutions of some fractional differential systems with different orders using the inverse operator method and Mittag–Leffler function. Moreover, the controllability of time-invariant linear fractional system is investigated. Some examples are provided to illustrate the theory.
Krishnan Balachandran +2 more
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Filtering for linear systems driven by fractional Brownian motion
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002In this paper we study continuous time filtering for linear multidimensional systems driven by fractional Brownian motion processes. We present the derivation of the optimum linear filter equations which involve a pair of functional-differential equations giving the optimum error covariance (matrix-valued) functions and the optimum filter.
Ahmed, N. U. +3 more
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The cauchy problem for linear nonstationary fractional systems
2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), 2017The paper is concerned with the existence and uniqueness of a solution to time variant linear fractional systems. We present representation of the solution in the form of series fractional integrals of the coefficients of the system. We prove uniform converges of this series. The considerations are illustrated by example.
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Minimum Energy Control of Fractional Linear Systems
2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR), 2018In the paper linear fractional finite-dimensional stationary damped dynamical control systems are considered. Under controllability assumption minimum energy control problem is formulated and analytically solved using properties of scalar product and norm in the finite dimensional space. The possible extensions are also pointed out.
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