This paper is devoted to the study of the flatness property of linear time-invariant differential systems of fractional systems. We give two characterizations of fractionally flat outputs and algorithms to compute them. We then present an application to a two dimensional thermal system that we approximate by a fractional model of order 1 2 , that is fractionally flat. Trajectory planning of the...

The chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor ...

In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigate...

In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI...

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case. The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of no...

Abstract: New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is d...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behaviour can be found in engineering, management scie...