Theorems on Implicit Lyapunov-Razumikhin functions (ILRF) for asymptotic, exponential, finite-time and nearly fixed-time stability analysis of nonlinear time-delay systems are presented. Based on these results, finite-time stabilization of a special class of such systems is addressed. These systems are represented by a chain of integrators with a timedelay term multiplied by a function of instantaneous state vector. Possible explicit restriction on nonlinear time-delay terms is discussed. Simple procedure of control parameters calculation is given in terms of linear matrix inequalities (LMIs). Some aspects of digital implementations of the presented nonlinear control law are touched upon. Theoretical results are illustrated by numerical simulations.

The paper considers the investigation of a novel robust control algorithm of an electric generator with unknown parameters under bounded disturbances and high-frequency measurement noises. It is assumed that only the load angle is available for measurement, but not the rotor speed. The electric generator model is described by a system of third-order nonlinear differential equations with algebraic coupling ones. The proposed algorithm consisting of static and dynamical terms is based on the separation of the filtering and estimating properties. Differently from existing results the proposed scheme provides the opportunity to control independently the quality of filtering and stabilization. Investigations show that the proposed algorithm attenuates parametric uncertainties and disturbances with accuracy that can be reduced by tuning algorithm parameters.

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The problem of multi-machine power system synchronization under parameter uncertainties, emergency modes, and measurement errors is considered. Only power angles of generators corrupted by bounded measurement errors are available for measurement. Emergency modes are associated with the sudden change of reactance of transmission lines. The proposed control law is based on measurement error filtering and left-differences estimation of power angel derivatives. Differently from some recent control schemes, it makes the obtained control law easier to tune and less sensitive to measurement errors. The robust-adaptive control law is suggested under unknown nominal values of reactances, EMFs, and currents. The simulations and experiments illustrate the efficiency of the proposed algorithm and confirm theoretical results in comparison with some existing ones.