Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems

2018 ◽  
Vol 112 ◽  
pp. 31-35 ◽  
Author(s):  
Chong Lin ◽  
Bing Chen ◽  
Peng Shi ◽  
Jin-Peng Yu
Keyword(s):  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Necessary And Sufficient

scholarly journals Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach

2020 ◽  
Vol 4 (1) ◽  
pp. 8
Author(s):  
Xuefeng Zhang ◽  
Yuqing Yan
Keyword(s):  
Fractional Order ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Fractional Order Systems ◽  
Lmi Approach ◽  
Numerical Examples ◽  
Necessary And Sufficient

This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils 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 some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

scholarly journals Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm

2011 ◽  
Vol 21 (3) ◽  
pp. 287-298 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Equations ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

Checking of the positivity of descriptor linear systems by the use of the shuffle algorithmNecessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. The shuffle algorithm is applied to transform the state equations of the descriptor systems to their equivalent form for which necessary and sufficient conditions for their positivity have been derived. A procedure for checking the positivity of the descriptor systems is proposed and illustrated by numerical examples.

scholarly journals The Oscillation of a Class of the Fractional-Order Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qianli Lu ◽  
Feng Cen
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Analysis Method ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this,α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.

Overconvergence of series in generalized mittag-leffler functions

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Integral Equations ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Differential And Integral Equations

AbstractSeries defined by means of the three-parametric Mittag-Leffler functions, called also the Prabhakar functions, are considered in this paper. Their behaviour is investigated on the boundaries of the convergence domains. Necessary and sufficient conditions for their overconvergence are proposed. The corresponding results for series in Mittag-Leffler functions are discussed as a particular case. Such kind of results are motivated by the fact that the solutions of some fractional order differential and integral equations can be written in terms of series (or series of integrals) of Mittag-Leffler type functions.

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