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

Hongyu Ma; Dadong Tian; Mei Li; Chao Zhang; Hongyu Ma; Dadong Tian; Mei Li; Chao Zhang

doi:10.3934/mmc.2024014

Mathematical Modelling and Control

2024, Volume 4, Issue 2: 152-162. doi: 10.3934/mmc.2024014

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Research article

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

College of Information Science and Engineering, Shandong Agricultural University, Tai'an 271018, China

Received: 05 September 2023 Revised: 07 January 2024 Accepted: 04 February 2024 Published: 14 May 2024

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.
- 2-D switched nonlinear positive systems,
- impulsive effects,
- average dwell time,
- exogenous disturbances,
- time-varying delays
Citation: Hongyu Ma, Dadong Tian, Mei Li, Chao Zhang. Reachable set estimation for 2-D switched nonlinear positive systems with impulsive effects and bounded disturbances described by the Roesser model[J]. Mathematical Modelling and Control, 2024, 4(2): 152-162. doi: 10.3934/mmc.2024014

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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.

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