Reachable set bounding for 2-D singular Roesser systems with interval directional delays: Analysis and control

This paper addresses the problems of reachable set estimation and controller design for two-dimensional (2-D) singular Roesser systems with time-varying delays. We first decompose the system into dynamic- and algebraic-subsystems and formulate a bounding ellipsoid that contains the reachable set of the system. Based on a 2-D Lyapunov functional scheme, and by utilizing zero-type matrix equations, we then derive tractable algebraic conditions to ensure that the system is admissible and admits an ellipsoid that bounds the set of all system states subject to bounded exogenous disturbances. The design problem of a state-feedback controller that makes the closed-loop reachable set is confined within a prescribed ellipsoid is also addressed. The efficacy of the proposed method is demonstrated by numerical examples with simulations.