A homogeneity property of discrete‐time systems: Stability and convergence rates. (17th February 2019)

• Record Type: Journal Article
• Authors: Sanchez, Tonametl; Efimov, Denis; Polyakov, Andrey; Moreno, Jaime A.; Perruquetti, Wilfrid
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 8(2019)
• Page Start: 2406
• Page End: 2421
• Publication Date: 2019-02-17
• Subjects: discrete‐time systems -- homogeneous systems -- Lyapunov methods -- nonlinear systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4497
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: A new definition of homogeneity for discrete‐time systems is introduced. As in the continuous‐time case, the property can be verified algebraically in the transition map of the system, and it implies that a dilation of the initial conditions leads to a scaling of the trajectory. Stability properties and convergence rates of the system's solutions can be established by considering only the homogeneity degree. The existence of homogeneous Lyapunov and Lyapunov‐like functions is proven.