ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Stability and Stabilization of Nonlinear Continuous and Discrete Uncertain Systems with Modal Approach


Irina Efremovna Zuber

Eng. Sc. D.,
Leading Researcher
St. Petersburg State University ,
199034 St.Petersburg, Universitetskaya nab.7/9

Arkadii Khaimovich Gelig

Doctor of Engineering Science in Physics and Mathematics,
St. Petersburg State University ,
199034 St.Petersburg, Universitetskaya nab.7/9


In this paper we consider the system of differential equations for which the elements of object matrix are functions of the system state and time. These functions are perturbed by uncertain functionals. Using the spectral decomposition of the object matrix and the Lyapunov quadratic function with unit matrix we obtain the sufficient conditions of global exponential stability of the system considered. The similar system is studied in the case of scalar control, on the assumption that the distribution vector depends on the state. Using the modal approach in the condition of the uniform controllability we perform the synthesis of scalar control which provides the global exponential stability of closed loop system. Analogous results are obtained for discrete nonlinear uncertain systems with the same structure.



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