Absolute stability of control systems with differentiable nonlinearity in the vicinity of a program manifold
Sailaubay Zhumatov
Source abstract
We investigate the absolute stability of automatic control systems with differentiable nonlinearity in the vicinity of a given program manifold. The problem is studied for both scalar and vector nonlinearities. Sufficient conditions for absolute stability are derived using Lyapunov functions and the S-procedure. Additional restrictions on the derivatives of nonlinearities are employed to establish the negative definiteness of the Lyapunov function derivative. For systems with vector nonlinearities and matrix feedback coefficients, the stability conditions are expressed in terms of Sylvester inequalities. In the scalar case, frequency-domain criteria for absolute stability are also obtained. The results are illustrated by the Vyshnegradsky equation, demonstrating how differentiability conditions on the nonlinearity can strengthen the stability criteria for nonlinear control systems.
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