Related papers: Fractional-Order State Space Models
The celebrated GKYP is widely used in integer-order control system. However, when it comes to the fractional order system, there exists no such tool to solve problems. This paper prove the FGKYP which can be used in the analysis of problems…
This paper proposes an original solution to input saturation and dead zone of fractional order system. To overcome these nonsmooth nonlinearities, the control input is decomposed into two independent parts by introducing an intermediate…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
In this paper the fractional order logistic map in the sense of Caputo's fractional differences is numerically approached. It is shown that the necessary iterations number to avoid transients must be of order of thousand, not of order of…
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations.
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…