Reachable set estimation for singular systems via state decomposition method

Abstract This paper is concentrated on the reachable set estimation (RSE) issue of singular systems with or without delays under zero initial conditions and bounded peak disturbances. The objective is to obtain an ellipsoid that containing all states beginning with the origin and to obtain less conservative RSE criteria with few decision variables. An augmented Lyapunov–Krasovskii functional (LKF) of the singular system with time-varying delays is designed in line with decomposed state vectors. Then the Wirtinger-based inequality along with the extended reciprocally convex matrix approach are employed to estimate the derivative of LKF. And the adopted equivalent transformation condition is with more general form. Consequently, a RSE criterion is obtained with less conservativeness as well as low computational demand. Specially, the RSE problem of singular systems without delays is considered by applying the state decomposition method. Finally, the superiority of the adopted methods are demonstrated by numerical examples.