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New noise‐to‐state stability and instability criteria for random nonlinear systems
Author(s) -
Yao Liqiang,
Zhang Weihai
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4773
Subject(s) - lemma (botany) , instability , nonlinear system , noise (video) , control theory (sociology) , stability (learning theory) , mathematics , state (computer science) , stability theory , affine transformation , function (biology) , computer science , pure mathematics , physics , algorithm , artificial intelligence , control (management) , ecology , poaceae , quantum mechanics , machine learning , evolutionary biology , mechanics , image (mathematics) , biology
Summary This paper investigates the noise‐to‐state stability and instability criteria for random nonlinear affine systems. Firstly, some new noise‐to‐state stability theorems, which weaken the sufficient conditions in the existing stability criteria on random nonlinear systems, are given by means of the uniformly asymptotically stable function. Secondly, the noise‐to‐state instability definitions are introduced and the sufficient conditions of noise‐to‐state instability are provided based on a new established lemma and the uniformly asymptotically stable function. Finally, some examples show the feasibility of theoretical findings.