ALGORITHM OF DETERMINATION OF NON-STATIONARY NONLINEAR SYSTEMS FULL STABILITY AREAS
https://doi.org/10.32362/2500-316X-2017-5-6-55-72
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.
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Review
For citations:
Berdnikov V.P. ALGORITHM OF DETERMINATION OF NON-STATIONARY NONLINEAR SYSTEMS FULL STABILITY AREAS. Russian Technological Journal. 2017;5(6):55-72. (In Russ.) https://doi.org/10.32362/2500-316X-2017-5-6-55-72
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