High-Gain Observers for a Class of Nonlinear Systems with Simultaneous and Different Delay at State, Input and Output

If in control systems, for any reason, such as cost limitation and environmental conditions, the states of the system could not be measured by measurement sensors, suitable observer should be designed for state estimation. In this paper, a high-gain observer for a class of nonlinear systems in triangular form with divers and simultaneous delay at state, input and output equations is proposed. If time delays are known, sufficient conditions are provided by using Lyapunov-Krasovskii theorem that guarantees the state estimation error converges asymptotically to zero. Conditions are expressed in this way that the output time delay is smaller than the defined amount and also the high-gain parameter in the observer structure is larger than the specified values. Simulation results on inverted pendulum with dc motor control illustrate the effectiveness of the proposed observer.