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Título del libro: Encyclopedia Of Systems And Control Engineering
Título del capítulo: Homogeneous Nonlinear Systems

Autores UNAM:
JAIME ALBERTO MORENO PEREZ;

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Autores externos:

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Idioma:

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Año de publicación:
2025

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Palabras clave:

Backstepping for homogeneous system; Control Lyapunov function; Control-Lyapunov functions; Finite time stability; Homogeneous approximation; Homogeneous feedback control; Homogeneous observer design; Homogeneous observers; Homogeneous system; Observers designs; Scaling properties; Stability analyze; Weighted homogeneity

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Resumen:

© 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.Homogeneity, or dilation symmetry, is a fundamental concept in control theory that facilitates the analysis and control design of nonlinear systems through scaling properties. This chapter presents a comprehensive overview of homogeneous systems, detailing their mathematical definitions, key properties, and historical development. Beginning with the foundational principles of weighted homogeneity, we explore its implications for stability analysis, control synthesis, and observer design. Notably, the chapter emphasizes the unique property of homogeneous systems where local stability implies global stability, significantly simplifying the stability proofs for complex nonlinear systems. We also discuss several advanced control techniques tailored for homogeneous systems, such as homogeneous Control Lyapunov Functions (CLFs), backstepping methods, and sliding mode control. The chapter further extends to output feedback control and homogeneous observer design, showcasing the versatility of the homogeneity framework in dealing with state estimation and partial state information scenarios. To support practical application, we provide illustrative examples and highlight seminal contributions from the literature. Through this structured exposition, the chapter underscores the pivotal role of homogeneity in both theoretical and practical control design, offering readers a thorough understanding of this powerful concept and its broad applicability. This contribution aims to serve as a reference point for researchers and practitioners seeking to leverage homogeneity for robust and efficient control of nonlinear systems.

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Entidades citadas de la UNAM:

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Fuente:


ISBN:
9780443140815
Editorial:
Elsevier

Tipo de producto:
Book chapter

DOI:
10.1016/B978-0-443-14081-5.00153-7