Sampled-Data Control of Nonlinear Oscillations Based on LMIs and Fridman's Method

Emilia Fridman's method based on time-dependent Lyapunov-Krasovsii functionals is extended to nonlinear control systems with sector bounded nonlinearity. Furthermore, this paper considers sampled-data feedback control under uncertain sampling with the known upper bound on the sampling intervals, where the control function is multiplied by bounded scalar nonlinear function in system equation. This special case corresponds to many oscillator control systems, for example, cart-pendulum system. The problem is reduced to feasibility analysis of linear matrix inequalities based on classical results of V.A. Yakubovich about S-procedure.