Fractional Differential-algebraic Systems Research Articles

Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative

Linear impulsive fractional differential-algebraic systems (LIFDAS) in a finite-dimensional space are studied. We obtain the solution of LIFDAS. Using Gramian matrices, necessary and sufficient conditions for controllability and observability of time-varying LIFDAS are established. We acquired criterion for time-invariant LIFDAS in the form of rank conditions. The results are more generalized than the results that are obtained for various differential-algebraic systems without impulses

On the Existence and Uniqueness of the Solution of Linear Fractional Differential-Algebraic System

The existence and uniqueness of the solution of a new kind of system—linear fractional differential-algebraic equations (LFDAE)—are investigated. Fractional derivatives involved are under the Caputo definition. By using the tool of matrix pair, the LFDAE in which coefficients matrices are both square matrices have unique solution under the condition that coefficients matrices make up a regular matrix pair. With the help of equivalent transformation and Kronecker canonical form of the coefficients matrices, the sufficient condition for existence and uniqueness of the solution of the LFDAE in which coefficients matrices are both not square matrices is proposed later. Two examples are given to justify the obtained theorems in the end.

H∞Control of Fractional Nonlinear Differential Systems

In this paper, the stabilization of nonlinear fractional differential algebraic system is constructed. The fractional nonlinear differential algebraic systems (FNDAS) in presence of disturbance, we construct a fractional control strategy. The proposed stabilization and robust controller effectively take advantage of the structural characteristics of FNDAS and is simple in form.

Controllability, Observability, Duality for Fractional Differential-Algebraic Systems with Delay

The paper deals with problems of relative controllability and Rn1 - observability for linear stationary fractional differential-algebraic system with delay (FDAD). FDAD system consists of fractional differential in the Caputo sense and difference equations. We present control systems and observation systems. We introduce the determining equation systems and their properties. By solution representations into series of their determining equation solutions we obtain effective parametric rank criteria for relative controllability and Rn1 -observability. A dual controllability result is also formulated.

Representation of solutions for fractional differential-algebraic systems with delays

Representation of solutions for fractional differential-algebraic systems with delays