In this paper the linear fractional representation problem of systems with rational parametric uncertainty is revisited from a multidimensional systems perspective. It is shown how this problem can be solved using the elementary operations approach. The minimality of the linear fractional representations obtained using this approach and other methods will be discussed. An example is presented t...

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and ...

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...

This paper deals with fractional order systems parameters estimation by use of Co-evolutionary Particle Swarm Optimization (CPSO) method. in some cases such as fractional order systems identification in spite of existing different methods, it is difficult to obtain estimation of model structure parameters and generally it leads to solving the with constrained complex non-linear optimization pro...

In this contribution, fractional-order controllers of the type PDμ and PIλ are applied to a class irrational transfer function models that appear in large-scale systems, such as networks mechanical/electrical elements distributed parameter systems. More precisely, by considering controller k p + η s α Laplace domain with − 1 ≤ , stability analysis parameter-space ( ) is presented. Furthermore, ...

In this paper, a new comparative approach has been proposed for reliable controller design. Scientists and engineers are often confronted with the analysis, design, and synthesis of real-life problems. The first step in such studies is the development of a 'mathematical model' which can be considered as a substitute for the real problem. The mathematical model is used here as a plant. Fractiona...