This paper focuses on mean exponential stability and $L_1$-gain analysis for nonlinear positive Markov jump systems (NPMJSs) based on a switching transition probability (STP), where sector nonlinear functions and delays are adopted. By developing a nonlinear stochastic copositive Lyapunov–Krasovskii functional (NSCLKF) approach, a sufficient condition for mean exponential stability of nonlinear positive time-delay Markov jump system is first presented under mode-dependent average dwell time (MDADT) switching by using linear programming (LP) approach. Further, $L_1$-gain performance analysis is obtained. Moreover, the corresponding results for NPMJSs are given under average dwell time (ADT) switching. Illustrative results are provided to verify the validity of the theoretical results.

本文着重于平均指数稳定性和${\mathrm{大号}}_1$-基于切换转换概率（STP）的非线性正马尔可夫跳跃系统（NPMJS）的增益分析，其中采用扇区非线性函数和延迟。通过开发非线性随机共正 Lyapunov-Krasovskii 泛函 (NSCLKF) 方法，首次使用线性规划在模式相关平均停留时间 (MDADT) 切换下提出了非线性正时滞马尔可夫跳跃系统平均指数稳定性的充分条件。 LP) 方法。进一步，${\mathrm{大号}}_1$-获得性能分析。此外，在平均停留时间 (ADT) 切换下给出了 NPMJS 的相应结果。提供了说明性结果以验证理论结果的有效性。