Robust adaptive control for system with unknown time varying delay

In this work, we propose a new robust adaptive sliding control mode law for power system with time varying state delay. The power system is a seventh order synchronous machine infinite bus system. The linearized model of the system belongs to a class of uncertain linear systems with unknown time varying state delay. In this work, disruption and uncertainty are assumed to be unknown. Hence, an upper limit has been determined. Accordingly, new control law for this kind of systems has been defined based on a Lyapunov function choice. This new approach consists of two steps; the first one is that the conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices. The second step is the determination of the control law based on a sliding surface that will converge to zero and estimate of the upper limit of the disturbance and uncertainties. This new control law has been validated in simulation on an uncertain numerical system and comparative study proved the efficiency of the proposed resulting methodology.