受多随机噪声和多随机脉冲干扰的非线性系统稳定性分析

Stability analysis of nonlinear system suffering from multiple random noises and multiple random impulses

针对一类受多有色噪声和多随机脉冲干扰的非线性系统(其中系统连续动态中的多随机噪声包含乘性和加性有色噪声且离散动态中多随机脉冲幅值的类型由一个齐次不可约非周期Markov链决定),分别提出概率意义和矩意义下的噪声-状态稳定性、概率意义下的全局渐近稳定性、矩意义下的指数稳定性判据.在脉冲数量受模态依赖平均脉冲区间约束下,首先基于乘性随机噪声的估计和Lyapunov函数方法,分别研究系统在矩意义下的噪声到状态稳定性和指数稳定性判据;然后基于乘性随机噪声满足大数定律的假设和Lyapunov函数方法,分别给出系统在概率意义下的噪声-状态稳定和全局渐近稳定的充分条件;最后通过仿真结果验证所提出稳定性判别准则的有效性.

For a class of nonlinear systems disturbed by multiple random noises and multiple random impulses, where the multiple random noises in continuous dynamics are composed of multiplicative and additive noises and the kind of multiple random impulsive amplitudes in discrete dynamics are driven by the Markov chain, this paper proposes the criteria of the noise-to-state stability in probability and in m-th moment, the global asymptotic stability in probability and the exponential stability in m-th moment, respectively. When the impulsive number is constrained by the mode-dependent average impulsive interval, firstly, the noise-to-state stability and exponential stability in m-th moment are investigated based on the estimation of multiplicative random noise, respectively. Then, on the basis of the assumption that the multiplicative random noise satisfies the law of large numbers, the sufficient conditions of the noise-to-state stability and global asymptotic stability in probability are given, respectively. Finally, the effectiveness of the proposed stability criteria is verified by the simulation results.