Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Systems Theory

Background:

• Fractional-order systems are increasingly used in various applications.
• Ensuring stability in systems with interval coefficients and time delays is challenging.
• Robust stability analysis is critical for reliable system performance.

Purpose of the Study:

• To develop a robust stability criterion for fractional-order systems with interval coefficients and time-delay.
• To provide sufficient and necessary conditions for determining the stability of such systems.
• To avoid redundant calculations in stability analysis.

Main Methods:

• Utilizing the Minkowski Sum to determine the vertices of the value set for the characteristic function.
• Defining a function to ascertain the positional relationship between the origin and the value set.
• Applying the zero exclusion principle to derive stability conditions.

Main Results:

• A novel method for identifying the vertices of the value set without redundant calculations.
• A defined function effectively represents the origin's position relative to the value set.
• Sufficient and necessary conditions for robust stability of the considered fractional-order systems are established.

Conclusions:

• The proposed method effectively determines the robust stability of fractional-order systems with interval coefficients and time-delay.
• The derived conditions are both necessary and sufficient, offering a precise stability analysis.
• Illustrative examples confirm the practical applicability and effectiveness of the developed criterion.