Abstract
The paper proposes a numerical algorithm for constructing piecewise linear Lyapunov functions for investigating the absolute stability of nonlinear nonstationary systems. Such functions define necessary and sufficient conditions for the stability of nonlinear nonstationary systems satisfying sector constraints. In the case of asymptotic stability of the system, the implementation of the algorithm will lead to the construction of the Lyapunov function level set in the form of a polyhedron of dimension equal to the dimension of the original system. Such a polyhedron can be used for constructing a piecewise linear Lyapunov function. The number of faces of the polyhedron increases as the system approaches to the stability boundary in the parameter space, which can lead to unacceptable time costs for calculations. The analysis of specific systems of the 2nd and 3rd order and the results of comparison with classical methods are given. Specific recommendations on the algorithm initial conditions choice are given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
