Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems

Hassanzadeh, Iman

doi:10.1016/j.isatra.2017.03.006

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…It is a powerful tool to describe systems which have long-term memory and longrange spatial interaction. Fractional calculus has been applied in control theory in recent years, and there have been many theoretical achievements in controllability [1,2], observability [3,4], stability [5][6][7], robustness [8,9] and control methods [10][11][12]. At the same time, fractional order theory has also achieved great success in control engineering, such as the fractional order PID controller [13,14], air-based precision positioning system [15], fractional order positive position feedback compensator [16], and fractional order gray model [17,18].…”

Section: Introductionmentioning

confidence: 99%

Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function

Bai

Xue

2022

Fractal Fract

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This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming an EFOTF into an equivalent fractional order differential equation, its time domain response can be obtained by solving the equation by the difference method. IFOTF cannot be transformed into an equivalent equation, so its time domain response cannot be calculated by existing difference methods. A new numerical algorithm is designed for calculating a convolution and its inverse operation, the time domain response of IFOTF can be calculated based on the algorithm. Error analysis shows that the proposed numerical algorithms are of first-order accuracy. Four calculation examples are presented, and the results are consistent with the theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function

Bai

Xue

2022

Fractal Fract

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Obtaining Controllable Pseudo-Upper and Lower Triangular Multi-Order State-Space Realizations from a Special Case of Incommensurate Fractional-Order Transfer Functions

Tabatabaei

2024

Circuits Syst Signal Process

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A new fractional collocation method for a system of multi-order fractional differential equations with variable coefficients

Faghih

Mokhtary

2021

Journal of Computational and Applied Mathematics

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Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems

Cited by 4 publications

References 32 publications

Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function

Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function

Obtaining Controllable Pseudo-Upper and Lower Triangular Multi-Order State-Space Realizations from a Special Case of Incommensurate Fractional-Order Transfer Functions

A new fractional collocation method for a system of multi-order fractional differential equations with variable coefficients

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