Investigation of stability of large-scale systems on the basis of Lyapunov's matrix functions
Copyright policy )Investigation of stability of large-scale systems on the basis of Lyapunov's matrix functions
The paper is a development of the Lyapunov matrix function approach and motion stability analysis of the nonlinear systems presented earlier by the first author and M. Z. Djordjevic [e.g.: \textit{M. Z. Djordjevic}, Syst. Control Lett. 3, 165-169 (1983; Zbl 0511.93051); the first author, Prikl. Mekh., Kiev 21, No.4, 89-96 (1985; Zbl 0597.70022)]. Decomposition of a large-scale system and the stability of the equilibrium state of the subsystems are shown in the first part of the paper. Stability criteria (sufficient stability and instability conditions and asymptotic stability conditions) are obtained in terms of the sign-definiteness of the special matrices. The authors consider also the perturbed motion of the linear system with nonlinear couplings. The paper is of theoretical character and should be of interest for researchers in the field of stability of nonlinear systems.
sufficient stability, Stability criteria, Stability for nonlinear problems in mechanics, Decomposition of a large-scale system, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Stability theory for smooth dynamical systems, stability analysis, stability of the equilibrium state, linear system with nonlinear couplings, instability conditions, nonlinear systems, Lyapunov matrix function, asymptotic stability conditions
sufficient stability, Stability criteria, Stability for nonlinear problems in mechanics, Decomposition of a large-scale system, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Stability theory for smooth dynamical systems, stability analysis, stability of the equilibrium state, linear system with nonlinear couplings, instability conditions, nonlinear systems, Lyapunov matrix function, asymptotic stability conditions
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