Robust Stability Of Fractional-order Systems Research Articles

Robust stability of fractional-order systems with mixed uncertainties: The [formula omitted] case

This paper addresses the problems of robust stability of fractional-order systems with mixed uncertainties, including multi-parameter uncertainties and norm-bounded uncertainties. The problems are relevant because on the one hand, uncertainties are common in real systems and the uncertainties in different components of systems may be of different types, and on the other hand, the non-convex and decoupling problems for fractional-order systems with α∈(0,1) and mixed uncertainties need to be thoroughly resolved. The core approaches utilized in this paper include the robust nonsingularity analysis of uncertain matrices, error-free determinant transformation and μ-analysis methods. Based on the above approaches, necessary and sufficient conditions for the robust stability of fractional-order systems with mixed uncertainties are proposed. Then, by estimating the spectral radius of the uncertain matrices, novel robust stability conditions for such uncertain fractional-order systems are obtained. After that, the robust stability bounds for such uncertain fractional-order systems are established, based on which an algorithm for solving the robust stability bounds is provided by utilizing the traversal method in the finite frequency interval. The derived results in this paper are more universal and less conservative than the existing works. Finally, two numerical examples including a fractional-order electrical circuit example are provided to demonstrate the applicability and effectiveness of the developed methods.

Novel robust stability conditions of fractional-order systems with structured uncertain parameters based on parameter-dependent functions: the 0

ABSTRACT In this paper, the robust stability of fractional-order systems with fractional order and structured uncertain parameters is considered. Firstly, novel robust stability conditions of the above systems are presented based on the parameter-dependent polynomial functions. Secondly, the existence of the parameter-dependent polynomial functions is transformed into linear matrix inequalities via the generalized Kalman-Yakubovič-Popov lemma. In addition, the above methods can also be applied to solve the robust stability of fractional-order systems with structured uncertainties or polytopic uncertainties. Finally, numerical examples are presented to show the proposed methods are less conservative than the existing methods.

On robust stability of incommensurate fractional-order systems

This paper investigates the robust stability of fractional-order systems described in pseudo-state space model with incommensurate fractional orders. An existing non-conservative robust stability criterion for integer-order systems is extended to incommensurate-order fractional systems by using the generalized Nyquist Theorem. Some robust stability conditions for various uncertainty structures are proposed by employing the proposed criterion. Moreover, we focus on the interval uncertainty structure to discuss the conservatism of the common methods. A numerical example is provided to investigate that how the fractional-order of each pseudo-state can affect the robustness of the system. The effectiveness of the proposed methods is compared by applying them on the problem of space tether deployment with fractional-order control law.

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

This study investigates the robust stability of fractional-order systems with interval coefficients and a time-delay. By the Minkowski Sum, the vertices of value set with respect to the characteristic function of the investigated fractional-order system are offered, avoiding the calculations of the redundant vertices. Meanwhile, a function depending on the obtained vertices is defined to represent the position relationship between the origin and the value set. Based on the zero exclusion principle, we propose sufficient and necessary conditions to determine the robust stability of fractional-order systems with interval uncertain coefficients and a time-delay. Finally, illustrative examples are offered to verify the effectiveness of the proposed robust stability criterion.