In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic, constant rate and planar, the discrete switching between the modes is probabilistic and happens at boundary of the invariant regions, and the continuous states are not reset during switching. These aptly model piecewise linear behaviors of planar robots. Our main result is an exact algorithm for deciding absolute and almost sure stability of Planar PPCD under some mild assumptions on mutual reachability between the states and the presence of non-zero probability self-loops. Our main idea is to reduce the stability problems on planar PPCD into corresponding problems on Discrete Time Markov Chains with edge weights.

翻译：在本文中,我们研究了对随机混合系统子类的概率稳定性分析,称为“Planar Pisbiotic Pacewith Constantical Systems (Planar PPCD) ”, 其连续动态是确定性、恒定率和平面,不同模式之间的离散转换是概率性的,发生在变化地区的边界,连续状态在转换过程中没有重新设定。这些适合的模型是板块式机器人的细线性行为。我们的主要结果是精确的算法,在各州之间对相互可及性和非零概率自我流失的某种微小假设下,决定Planar PPCD的绝对性和几乎肯定稳定性。 我们的主要想法是减少Planar PPCD的稳定性问题,将其转化为具有边缘重量的断裂时马可链的相应问题。