Browsing by Author "Ates, Muzaffer"

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Belirli Üçüncü Mertebeden Doğrusal Olmayan Vektörel Diferansiyel Denklemlerin Global Asimptotik Kararlılığı Üzerine Yeni Sonuçlar
(2017) Ates, Muzaffer
Bu çalışmanın amacı, belirli üçüncü mertebeden doğrusal olmayan vektörel diferansiyel denklemlerin global asimptotik kararlılığını garanti etmek için yeterli şartları vermektir. Bu çalışmada sunulan sonuçlar önceden yayınlanmamış ve literatürdeki mevcut bazı sonuçları geliştirmiştir. Ana sonuçlarımızı resimlemek için basit bir örnek de verilmiştir
Boundedness of Solutions To Differential Equations of Fourth Order With Oscillatory Restoring and Forcing Terms
(Hindawi Ltd, 2013) Tunc, Cemil; Ates, Muzaffer
This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded. Copyright (C) 2013 C. Tunc, and M. Ates.
Circuit Theory Approach To Stability and Passivity Analysis of Nonlinear Dynamical Systems
(Wiley, 2022) Ates, Muzaffer
In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear time-varying systems controlled by a second-order vector differential equation. First, we obtain this equation from a nonlinear time varying network of the circuit theory. Then, we construct the Lyapunov candidate function directly from the physical meaning of the given system. By the way, we review a number of previous results from the point view of Lyapunov's direct method. Our system with its real energy function generalize and improve upon some well-known studies. The new concept facilitates the formulation of the energy (Lyapunov) function from the power-energy relationship of the given system. Then, we also realized that the time derivative of the Lyapunov function for a given dynamical systems is the negative value of the power dissipated in the system. Therefore, with the proposed approach, one can inspect the result of the time derivative of the energy function for a given physical system. Finally, two examples (one with simulations) are used to illustrate the superiority and validity of the obtained results.
Instability of Certain Nonlinear Differential Equations of Fifth Order
(indonesian Mathematical Soc, 2016) Tunc, Cemil; Ates, Muzaffer
This paper establishes certain sufficient conditions to guarantee the nonexistence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.
New Results on the Global Asymptotic Stability of Certain Nonlinear Rlc Circuits
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ates, Muzaffer; Laribi, Samira
This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.
On the Global Stability Properties and Boundedness Results of Solutions of Third-Order Nonlinear Differential Equations
(Hindawi Ltd, 2013) Ates, Muzaffer
We studied the global stability and boundedness results of third-order nonlinear differential equations of the form x + psi(x,(x) over dot,x)x + f(x,x,x) = P(t,x,x,x). Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with P equivalent to 0 and the other with P not equal 0. The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results.
Power System Stability Analysis by Lyapunov Method
(2023) Alı, Rodı Ayıd Alı; Ates, Muzaffer
ÖZET LYAPUNOV YÖNTEMİ İLE GÜÇ SİSTEMİ KARARLILIK ANALİZİ ALI, Rodi Ayid Yüksek Lisans Tezi, Elektrik ve Elektronik Mühendisliği Anabilim Dalı Danışmanı Doç. Dr. Muzaffer ATEŞ Eylül 2023, 59 sayfa Güç sisteminin kararlılığı, modern güç sistemi ağlarında en zorlu ve önemli konulardan biridir. Güç sisteminden bu yana, kararlılık, elektrik güç sisteminin yük tarafına ve müşterilere iletilmesi ve teslim edilmesinin verimliliğini etkilemektedir. Güç sistemi kararlılığı analizi ve geliştirmesi, mühendisliğin en iyi sistemi tasarlaması için temel sorun olmuştur. Güç sistemi kararlılığını analiz etmek için en güçlü araçlardan biri Lyapunov kararlılık yöntemidir. Lyapunov yöntemi bu çalışmada hem enerji üretim sisteminde hem de iletim hatlarında aynı amaçla kullanılmıştır. Makalenin yeniliği, Lyapunov enerji fonksiyonu kararlılık yönteminin, tekli ve çok makineli sistemler, güç sistemi kararlılığı ile bir LC devresi arasındaki ilişki ve hem π- iletim hatlarının kararlılık analizi dahil olmak üzere güç sistemlerinin çeşitli yönlerine uygulanmasında yatmaktadır. Lyapunov stabilite yöntemi π-tip ve T-tipi. Bu katkılar, Lyapunov'un matematiksel yaklaşımını kullanan güç sistemlerinin kararlılık davranışına ilişkin değerli bilgiler sunmaktadır. Anahtar kelimeler: Çok makineli kararlılık, Enerji nakil hatları, Geçici kararlılık, Güç sistemi, Kararlılık analizi, Lyapunov yöntemi, Tek makineli kararlılık
Stability and Boundedness Results for Solutions of Certain Third Order Nonlinear Vector Differential Equations
(Springer, 2006) Tunc, Cemil; Ates, Muzaffer
In this paper, we investigate the asymptotic stability of the zero solution and boundedness of all solutions of a certain third order nonlinear ordinary vector differential equation. The results are proved using Lyapunov's second (or direct method). Our results include and improve some well known results existing in the literature.
Stability and Passivity Analysis of Higher-Order Differential Systems Inspired by Rlc Circuits
(Wiley, 2024) Ates, Muzaffer; Ates, Muhammet
This paper discusses the global asymptotic stability and strong passivity analysis of fourth-order nonlinear and time-varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non-linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time-varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's linearization method. The relationship between stability and passivity is also given. Meanwhile, we realized that linear system analysis is not a guaranteed way for determining the stability properties of a full system. Finally, the correctness and availability of the proposed approach are verified through simulation results.