具有随机时变滞后系统的稳定性

New Sufficient Stability Criteria for a Linear Engineering System with Randomly TimeVarying Delays

利用李雅普诺夫—拉祖米亨泛函，给出了一类具有随机时变滞后的随机系统零解几乎必然稳定及几乎必然渐近稳定的判别准则，讨论了此类大系统的分解问题，给出了大系统零解稳定的充分条件。

Almostsure sample stability of systems with randomly timevarying delays were studied for many years with stochastic Lyapunov function. Zhang used LyapunovRazumikhin stability conditions to derive sufficient stability criteria for Itotype systems . We extended the applicability of LyapunovRazumikhin conditions and succeeded in deriving new sufficient stability criteria for nonIto type linear engineering system. We employed Markov theory to give a rather long and complicated discussion of how to extend the applicability of LyapunovRazumikhin stability conditions to nonIto type of linear engineering systems with randomly timevarying delays. We decomposed a nonIto type largescale linear engineering system, mathematically expressed as eq.(1), into a family of isolated subsystems, mathematically expressed as eq.(5). Then we obtained eqs.(9), (12) and (13) as the new stability criteria of the system described by eq.(1). These criteria are related to the stabilities of the subsystems and to bounds on components interconnecting the subsystems. We took as example a system described by eq.(14) and used our approach to prove its almostsure stability.