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Updated: Jun 25, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Robust stability analysis of fractional order interval polynomials.

Nusret Tan¹, O Faruk Ozgüven, M Mine Ozyetkin

¹Inonu University, Engineering Faculty, Department of Electrical and Electronics Engineering, 44280, Malatya, Turkey. ntan@inonu.edu.tr

ISA Transactions

|February 6, 2009

Summary

This study introduces a new method for robust stability analysis of fractional order interval control systems. It addresses limitations of existing theorems by presenting a novel algorithm for fractional order interval polynomial stability testing.

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Last Updated: Jun 25, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

Control Systems Engineering
Nonlinear Dynamics
Mathematical Analysis

Background:

Robust stability analysis is crucial for control systems with uncertain parameters.
Fractional order systems and interval uncertainty present unique challenges not addressed by classical methods.
Existing stability theorems, like Kharitonov's, are not directly applicable to fractional order interval polynomials.

Purpose of the Study:

To develop a robust stability analysis method for fractional order interval polynomial (FOIP) families.
To address the limitations of existing theorems for Bounded Input Bounded Output (BIBO) stability testing in these systems.
To provide a practical algorithm for assessing the stability of fractional order interval control systems (FOICS).

Main Methods:

Demonstrating the inapplicability of the Kharitonov theorem to FOIPs.
Developing a procedure to compute the value set of FOIPs.
Presenting a stability testing algorithm based on the computed value set.

Main Results:

The Kharitonov theorem is shown to be unsuitable for FOIPs.
A method for calculating the value set of FOIPs is established.
A novel algorithm for robust stability testing of FOIPs is proposed and validated with examples.

Conclusions:

The developed algorithm provides a reliable method for stability analysis of FOIPs.
The findings are essential for the design and analysis of fractional order interval control systems.
The method effectively assesses the impact of parametric variations on system stability.