This paper investigates the exponential stability of some interconnected stochastic control systems with non-trivial equilibria, for which the considered interconnected systems are induced by the composition of some stochastic subsystems. Of particular interest is the notion of stability with respect to a set containing the non-trivial equilibria. It is shown that the exponential stability of the interconnected or composite feedback control systems can be deduced from the stability of the isolated subsystems. Using the preliminary results concerning practical exponential stability of continuous-time stochastic systems that without a common equilibria, we present sufficient conditions for practical exponential stability of the composite system based upon a computable feedback law that would also render the set containing all non-trivial equilibrium solutions of each stochastic subsystem with the same stability. Finally, several illustrative examples are presented to show the applicability of the results.

本文研究了具有非平凡平衡的某些相互联系的随机控制系统的指数稳定性，为此，所考虑的相互联系的系统是由一些随机子系统的组成而产生的。特别令人感兴趣的是关于包含非平凡均衡的集合的稳定性的概念。结果表明，可以从隔离子系统的稳定性中推断出互连或复合反馈控制系统的指数稳定性。使用关于没有共同均衡的连续时间随机系统的实际指数稳定性的初步结果，我们基于可计算的反馈定律为复合系统的实际指数稳定性提供了充分的条件，该定律还将使包含每个随机子系统的所有非平凡平衡解的集合具有相同的稳定性。最后，给出了几个说明性的例子来说明结果的适用性。