This paper deals with stabilising uncertain Switched Positive Linear Systems (SPLSs) with a bumpless transfer controller. The contribution of this study is to improve switching controller robustness at the switching instances and also guarantee the $L_1$–gain performance of the positive systems. Positive systems are widespread; most of the biological, economic systems, disease, etc., have nonnegative variables belonging to this class of systems. Positive Systems modelling encounters different types of uncertainties; therefore, stability analysis and stabilisation of uncertain SPLSs are crucial in analysing positive systems. The stability of the SPLSs can be guarantee by using multiple copositive Lyapunov functions with the Dwell Time (DT) strategy. The stability of the SPLS has been investigated under synchronous and asynchronous switching modes. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. Also, the $L_1$–gain performance of the system is derived. Finally, two illustrative examples are provided to demonstrate the proposed scheme’s effectiveness compared with the foremost existing solutions.

本文处理使用无扰动传输控制器稳定不确定的开关正线性系统 (SPLS)。本研究的贡献是提高切换实例的切换控制器鲁棒性，并保证${\mathrm{大号}}_1$– 获得正系统的性能。积极的系统很普遍；大多数生物、经济系统、疾病等都有属于这类系统的非负变量。正系统建模遇到不同类型的不确定性；因此，不确定性 SPLs 的稳定性分析和稳定化对于分析正系统至关重要。通过使用具有驻留时间 (DT) 策略的多个正 Lyapunov 函数，可以保证 SPLS 的稳定性。已经在同步和异步切换模式下研究了 SPLS 的稳定性。所谓异步切换是指候选控制器和系统模式之间的切换是异步的。此外，该${\mathrm{大号}}_1$– 推导出系统的增益性能。最后，提供了两个说明性示例，以证明所提出的方案与最重要的现有解决方案相比的有效性。