On reachable set estimation of nonlinear singular systems with distributed delay

The estimation of the reachable set for singular systems with distributed delay and nonlinear term under zero initial condition is studied in this article. Based on the Lyapunov functional with triple integrals, a sufficient condition for bounding the reachable set is established by combining the free-weighting matrix method, the integral mean value theorem, and the new inequality scaling method. Then the reachable set of nonlinear singular system is bounded by the prescribed ellipsoids. Finally, two numerical examples and a practical example verify the validity of the theoretical analysis.