Relaxation of Conditions of Lyapunov Functions

Şahan, Gökhan

doi:10.19113/sdufenbed.808371

Relaxation of Conditions of Lyapunov Functions

Gökhan ŞAHAN (İzmir Yüksek Teknoloji Enstitüsü, Matematik Bölümü, İzmir, Türkiye)

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Yıl: 2021 Cilt: 25 Sayı: 2 Sayfa Aralığı: 238 - 244 Metin Dili: İngilizce DOI: 10.19113/sdufenbed.808371 İndeks Tarihi: 29-07-2022

Relaxation of Conditions of Lyapunov Functions

Öz:

In this study, stability conditions are given for nonlinear time varyingsystems using the classical Lyapunov 2nd Method and its arguments. A novelapproach is utilized and so that uniform stability can also be proved by using anunclassical Lyapunov Function. In contrast with the studies in the literature,Lyapunov Function is allowed to be negative definite and increasing through thesystem. To construct a classical Lyapunov Function, we use a reverse timeapproach methodology for the intervals where the unclassical one is increasing. Sowe prove the stability using a new Lyapunov Function construction methodology.The main result shows that the existence of such a function guarantees the stabilityof the origin. Some numerical examples are also given to demonstrate theefficiency of the method we use.

Anahtar Kelime: Lyapunov 2nd Method Uniform Stability Stability Analysis Lyapunov Function Time-varying Systems Nonlinear Systems

Lyapunov Fonksiyonun Koşullarının Gevşetilmesi

Öz:

Bu çalışmada, klasik Lyapunov 2. Metodu ve bu metoda dair argümanlar kullanılarak, zamanla değişen yapıdaki Doğrusal Olmayan Sistemler için kararlı olma koşulları verilmektedir. Özgün bir yaklaşım kullanılmış ve böylece düzgün kararlılık, klasik olmayan bir Lyapunov Fonksiyonu kullanılarak da ayrıca ispatlanabilmiştir. Literatürdeki çalışmaların aksine, kullandığımız klasik olmayan Lyapunov Fonksiyonunun bazı aralıklar için sistem boyunca artan ve negatif tanımlı olmasına izin verilmiştir. Klasik Lyapunov Fonksiyonu’nu inşaa etmek için, klasik olmayan Lyapunov Fonksiyonu’nun artan olduğu aralıklarda ters zaman yaklaşımını kullanıyoruz. Böylece yeni bir Lyapunov Fonksiyonu inşa etme yaklaşımı kullanarak kararlığı ispatlamış oluyoruz. Ana sonuç böyle bir fonksiyonun varlığının, orjinin kararlılığını garantilediğini gösterir. Yaklaşımın efektif olduğunu göstermek için ayrıca bir takım nümerik örnekler de verilmiştir

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Şahan G (2021). Relaxation of Conditions of Lyapunov Functions. , 238 - 244. 10.19113/sdufenbed.808371
Chicago	Şahan Gökhan Relaxation of Conditions of Lyapunov Functions. (2021): 238 - 244. 10.19113/sdufenbed.808371
MLA	Şahan Gökhan Relaxation of Conditions of Lyapunov Functions. , 2021, ss.238 - 244. 10.19113/sdufenbed.808371
AMA	Şahan G Relaxation of Conditions of Lyapunov Functions. . 2021; 238 - 244. 10.19113/sdufenbed.808371
Vancouver	Şahan G Relaxation of Conditions of Lyapunov Functions. . 2021; 238 - 244. 10.19113/sdufenbed.808371
IEEE	Şahan G "Relaxation of Conditions of Lyapunov Functions." , ss.238 - 244, 2021. 10.19113/sdufenbed.808371
ISNAD	Şahan, Gökhan. "Relaxation of Conditions of Lyapunov Functions". (2021), 238-244. https://doi.org/10.19113/sdufenbed.808371

APA	Şahan G (2021). Relaxation of Conditions of Lyapunov Functions. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 238 - 244. 10.19113/sdufenbed.808371
Chicago	Şahan Gökhan Relaxation of Conditions of Lyapunov Functions. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25, no.2 (2021): 238 - 244. 10.19113/sdufenbed.808371
MLA	Şahan Gökhan Relaxation of Conditions of Lyapunov Functions. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.25, no.2, 2021, ss.238 - 244. 10.19113/sdufenbed.808371
AMA	Şahan G Relaxation of Conditions of Lyapunov Functions. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2021; 25(2): 238 - 244. 10.19113/sdufenbed.808371
Vancouver	Şahan G Relaxation of Conditions of Lyapunov Functions. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2021; 25(2): 238 - 244. 10.19113/sdufenbed.808371
IEEE	Şahan G "Relaxation of Conditions of Lyapunov Functions." Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25, ss.238 - 244, 2021. 10.19113/sdufenbed.808371
ISNAD	Şahan, Gökhan. "Relaxation of Conditions of Lyapunov Functions". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25/2 (2021), 238-244. https://doi.org/10.19113/sdufenbed.808371