Observer Design for One-sided Lipschitz Uncertain Descriptor Systems with Time-varying Delay and Nonlinear Uncertainties

This paper investigates observer design for a class of one-sided Lipschitz descriptor systems with time-varying delay and uncertain parameters. In order to provide a general framework for large-scale systems, the paper considers uncertainties, nonlinearities, disturbance and time-varying delay at both output and state. By constructing Lyapunov–Krasovskii functional, and using the one-sided Lipschitz condition and the quadratic inner-boundedness inequality, we establish the sufficient condition which guarantees that the observer error dynamics is asymptotically stable, and the proposed observer ensures the $$L_2$$ gain bounded by a scalar $$\gamma .$$ Then, we change the condition into a strict matrix inequality condition. Furthermore, based on the obtained results, we establish the linear matrix inequality-based condition to ensure the asymptotically convergence of state estimation error and to accomplish robustness against $$L_2$$ norm bounded disturbances by utilizing change of variables. We propose the computing method of observer gain. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.