Novel Stability and Stabilization Conditions of Linear Fractional-Order Time-Delay Systems Using Free Matrix Approach

The stability and stabilization problem of linear fractional-order time-delay systems is investigated. By introducing a free matrix, the linear fractional-order time-delay systems is transformed to a delay-free system interconnected with uncertainties. New stability and stabilization criteria are derived based on the small gain theorem. The criteria are formulated as linear matrix inequalities and are computationally efficient. Since the free matrix is utilized, the new conditions are less conservative than the existing ones. Two numerical examples indicate that the proposed criteria are less conservative than existing ones.

Automated summary

The paper investigates the stability and stabilization problem of linear fractional-order time-delay systems. By introducing a free matrix, the systems are transformed into delay-free systems interconnected with uncertainties. New stability and stabilization criteria based on the small gain theorem are derived, expressed as linear matrix inequalities and computationally efficient. The proposed criteria are less conservative than existing ones, as shown in two numerical examples.