Control and synchronization of the financial systems with fractional-order are discussed in this paper. Based on the stability theory of fractional-order differential equations, Routh-Hurwitz stability condition, and by using linear control, simpler controllers are designed to achieve control and synchronization of the fractional-order financial systems. The proposed controllers are linear and ...

f(x1, . . . , xd) ∈ Ud (C) ⇐⇒ f(ıx1, . . . , ıxd) ∈ Hd(C) Consequently, many of the properties of H(C) follow immediately from the properties of U (C), and their proofs will be omitted. See [1–7, 13] for more information about U (C) and H(C). We use the notation in [7], and let RHP denote the right half plane. We do not cover well-known topics in one variable such as Routh-Hurwitz, the Edge the...

Chaos synchronization in some dynamical systems is studied in a general case. We use the boundedness of some dynamical systems, nonreplica approach to chaos synchronization and Routh-Hurwitz criteria to propose a simple method to make negative all the conditional Lyapunov exponents. The method is tested on the classical Lorenz model and one of Rossler models. Generalization of some features of ...

Absolute and Relative Stability. A control system is called absolutely stable if the controlled transfer function Hd(s) from the reference signal yd(s) to the output signal y(s) has all of its poles in the open left half plane. One technique for determining absolute stability of a control system is the Routh-Hurwitz stability analysis technique. This very useful technique is presented in Sectio...

In this work, we investigate the dynamical behavior of a fractional order cholera model. All the feasible equilibria for the system are obtained and the conditions for the existence of interior equilibrium are determined. Local stability analysis of the cholera model is studied by using the fractional Routh-Hurwitz stability conditions. Our results indicate the potential of fractional-order cho...

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh–Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendu...

In this research proposal, diminution of higher order (HO) discrete interval system (DIS) is accomplished by utilizing Kharitonov polynomials. The DIS firstly, transformed into continuous (CIS). Markov-parameters (MPs) and time-moments (TMs) are exploited for determination approximated models. ascertainment model (MOD) DISs done Routh-Padé approximation. Routh table utilized to obtain th...

Classical stability results and tests on the stability of a given polynomial are proved and derived here using a simple continuity property. The resulting new proofs given of the Hermite-Bielei theorem and the Routh and Jury tests are elementary and insightful. Most important, the proofs given here would allow the instructor to present these fundamental topics of control theory, for the first t...