Simultaneous stabilization of polynomial nonlinear systems via density functions
| Autor: | Alireza Khayatian, Peyman Kohan-sedgh, Navid Behmanesh-Fard |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Lyapunov function
0209 industrial biotechnology Polynomial Computer Networks and Communications Applied Mathematics 02 engineering and technology Stability (probability) Square (algebra) symbols.namesake Nonlinear system 020901 industrial engineering & automation Exponential stability Control and Systems Engineering Stability theory ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Signal Processing 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 020201 artificial intelligence & image processing Affine transformation Mathematics |
| Zdroj: | Journal of the Franklin Institute. 357:1690-1706 |
| ISSN: | 0016-0032 |
| DOI: | 10.1016/j.jfranklin.2019.11.033 |
| Popis: | This paper is concerned with simultaneous stabilization of a class of polynomial nonlinear systems with almost stability theory. The theory uses dual Lyapunov or density function criterion which has remarkable advantages over Lyapunov-based simultaneous stabilization. These advantages rely in convexity property of density functions. This property results in controller synthesis problems which are affine with respect to unknown polynomials variables. The results of almost stability are also extended to simultaneous asymptotic stability at the expense of adding some extra affine polynomial inequalities. Numerical method for verification of positivity of multivariate polynomials based on sum of square decomposition is used. Numerical examples and a fault tolerant design scheme are used to show the effectiveness of the proposed methods. |
| Databáze: | OpenAIRE |
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