Reachable set estimation for 2-D switched nonlinear positive systems with impulsive effects and bounded disturbances described by the Roesser model

Abstract

The reachable set estimation for two-dimensional (2-D) switched nonlinear positive systems (SNPSs) with bounded disturbances given by the Roesser model is investigated in this paper, in which both the time-varying delays and lagged impulsive effects are taken into account. By applying the average dwell time (ADT) technique, we provide a sufficient condition for the presence of a ball such that any solution of the system converges exponentially within it. An accurate estimate of the convergence rate is provided. We also extend the result to 2-D SNPSs with multi-directional delays, general 2-D switched linear systems, and 2-D SPNSs with heterogeneous delays. Finally, an example is worked out to demonstrate the effectiveness of the main result.

Keywords

• 2-d switched nonlinear positive systems
• impulsive effects
• average dwell time
• exogenous disturbances
• time-varying delays