scholarly journals Constrained Controllability of theh-Difference Fractional Control Systems with Caputo Type Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ewa Pawluszewicz
Keyword(s):  
Sufficient Conditions ◽  
Fractional Operator ◽  
Discrete Time System ◽  
Time System ◽  
Fractional Systems ◽  
Constrained Controllability ◽  
Fractional Differential ◽  
Target Set ◽  
Fractional Control ◽  
Necessary And Sufficient

The problem of controllability to a given convex target set of linear fractional systems withh-difference fractional operator of Caputo type is studied. Necessary and sufficient conditions of controllability with constrained controllers for such systems are given. Problem of approximation of a continuous-time system with Caputo fractional differential by a discrete-time system withh-difference fractional operator of Caputo type is discussed.

Multivariate Poisson flows on Markov step processes

1982 ◽  
Vol 19 (2) ◽  
pp. 289-300 ◽  
Author(s):  
Frederick J. Beutler ◽  
Benjamin Melamed
Keyword(s):  
Counting Process ◽  
Sufficient Conditions ◽  
Infinitesimal Operator ◽  
Negative Function ◽  
Rate Of Increase ◽  
Weakened Version ◽  
Target Set ◽  
Empty Target ◽  
Necessary And Sufficient ◽  
Mutually Independent

A Markov step process Z equipped with a possibly non-denumerable state space X can model a variety of queueing, communication and computer networks. The analysis of such networks can be facilitated if certain traffic flows consist of mutually independent Poisson processes with respective deterministic intensities λi (t). Accordingly, we define the multivariate counting process N = (N1, N2, · ·· Nc) induced by Z; a count in Ni occurs whenever Z jumps from x (χ into a (possibly empty) target set . We study N through the infinitesimal operator à of the augmented Markov process W = (Z, N), and the integral relationship connecting à with the transition operator Tt of W. It is then shown that Ni depends on a non-negative function ri defined on χ; ri (x) may be interpreted as the expected rate of increase in Ni, given that Z is in state x.A multivariate N is Poisson (i.e., composed of mutually independent Poisson streams Ni) if and only if simultaneous jumps are impossible in a certain sense, and if the conditional expectation E[ri (Z(t) | 𝒩i] = E[ri (Z(t))] for i = 1, 2, ···, c and each t ≧ 0, where 𝒩i is the σ-algebra σ{N(s), s ≦ t}. Necessary and sufficient conditions are also specified that, for each s ≦ t, the variates [Ni(t)-Ni(s)] are mutually independent Poisson distributed; this involves a weakened version of E[ri(Z(v)) | N(v) – N(u)] = E [ri(Z(v))] for i = 1, 2, ···, c and all 0 ≦ u ≦ v.It is shown that the above criteria are automatically met by the more stringent classical requirement that N(t) and Z(t) be independent for each t ≧ 0.

scholarly journals Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Wei Kang ◽  
Hao Chen ◽  
Kaibo Shi ◽  
Jun Cheng
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Reachable Set ◽  
Time Varying ◽  
Discrete Time System ◽  
Initial State ◽  
Time System ◽  
Time Varying Delay ◽  
Bounded Disturbance ◽  
Varying Delay

This paper investigates the problem of reachable set bounding for discrete-time system with time-varying delay and bounded disturbance inputs. Together with a new Lyapunov-Krasovskii functional, discrete Wirtinger-based inequality, and reciprocally convex approach, sufficient conditions are derived to find an ellipsoid to bound the reachable sets of discrete-time delayed system. The main advantage of this paper lies in two aspects: first, the initial state vectors are not necessarily zero; second, the obtained criteria in this paper do not really require all the symmetric matrices involved in the employed Lyapunov-Krasovskii functional to be positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

scholarly journals Stability of Stochastic Discrete-Time Neural Networks with Discrete Delays and the Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liyuan Hou ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Delays ◽  
The Stability

This paper investigates the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay. As the partition of time-varying and leakage delay is brought in the discrete-time system, we construct a novel Lyapunov-Krasovskii function based on stability theory. Furthermore sufficient conditions are derived to guarantee the global asymptotic stability of the equilibrium point. Numerical example is given to demonstrate the effectiveness of the proposed method and the applicability of the proposed method.

scholarly journals Positivity and stabilization of fractional 2D linear systems described by the Roesser model

2010 ◽  
Vol 20 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Roesser Model ◽  
Fractional Difference ◽  
Fractional Systems ◽  
New Class ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Positivity and stabilization of fractional 2D linear systems described by the Roesser modelA new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2DZ-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

scholarly journals Positifitas dan Ketercapaian Sistem Linier Fractional Waktu Kontinu

CAUCHY ◽  
2011 ◽  
Vol 2 (1) ◽  
pp. 18
Author(s):  
Imam Fahcruddin
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Fractional Systems ◽  
Necessary And Sufficient

<div class="standard"><a id="magicparlabel-2384">This paper studies a solution of the fractional continuous-time linier system. Necessary and sufficient condition were established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems. </a></div>

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Comparison of Different Models of Positive Fractional Continuous-Time Linear Systems and Electrical Circuits Based on the Step Responses

2017 ◽  
Vol 260 ◽  
pp. 147-155
Author(s):  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
State Equations ◽  
Electrical Circuits ◽  
Fractional Systems ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Step Responses

The step responses of positive fractional continuous-time linear systems and electrical circuits described by different models will be investigated and comparison of the models will be performed. Solutions to the state equations of continuous-time linear systems described by Caputo and Caputo-Fabrizio derivatives and necessary and sufficient conditions of the positivity of fractional systems will be recalled. Considerations will be illustrated by numerical examples.

Finite Difference Computational Method for Trajectory Controllability of a Delayed Damped System Governed by Fractional Differential Equation

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
P. Muthukumar ◽  
B. Ganesh Priya
Keyword(s):  
Finite Difference ◽  
Sufficient Conditions ◽  
Mathieu Equation ◽  
Computational Method ◽  
Scientific Models ◽  
Banach Fixed Point Theorem ◽  
Damped System ◽  
Fractional Differential ◽  
Necessary And Sufficient ◽  
System With Time Delay

In this paper, the trajectory controllability (T-controllability) of a nonlinear fractional-order damped system with time delay is studied. Existence and uniqueness of solution are obtained by using the Banach fixed point theorem and Green's function. Necessary and sufficient conditions of trajectory controllable for the nonlinear system are formulated and proved under a predefined trajectory. Modified fractional finite difference method is applied to the system for numerical approximation of its solution. The applicability of this technique is demonstrated by numerical simulation of two scientific models such as neuromechanical interaction in human snoring and fractional delayed damped Mathieu equation.

Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Triet Nguyen-Van ◽  
Noriyuki Hori
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Van Der Pol Oscillator ◽  
Discrete Time System ◽  
Time System ◽  
Time Model ◽  
Forward Difference ◽  
Discrete Time Models

An innovative approach is proposed for generating discrete-time models of a class of continuous-time, nonautonomous, and nonlinear systems. By continualizing a given discrete-time system, sufficient conditions are presented for it to be an exact model of a continuous-time system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discrete-time models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and space-filling oscillations even for large sampling periods, and out-performs the forward difference model, which is a well-known, widely-used, and on-line computable model.

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