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New Insights on One-Sided Lipschitz and Quadratically Inner-Bounded\n Nonlinear Dynamic Systems

2020/02/06 by Sebastian A. Nugroho, Vu Hoang, Nugroho, Sebastian A. +7
Engineering · #Adaptive Control of Nonlinear Systems #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.2002.02361

openalex publication_date 2020/02/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Nonlinear dynamic systems can be classified into various classes depending on\nthe modeled nonlinearity. These classes include Lipschitz, bounded Jacobian,\none-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes\nessentially yield bounding constants characterizing the nonlinearity. This is\nthen used to design observers and controllers through Riccati equations or\nmatrix inequalities. While analytical expressions for bounding constants of\nLipschitz and bounded Jacobian nonlinearity are studied in the literature, OSL\nand QIB classes are not thoroughly analyzed---computationally or analytically.\nIn short, this paper develops analytical expressions of OSL and QIB bounding\nconstants. These expressions are posed as constrained maximization problems,\nwhich can be solved via various optimization algorithms. This paper also\npresents a novel insight particularly on QIB function set: any function that is\nQIB turns out to be also Lipschitz continuous.\n

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