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. Our experimental results on planar robots with faulty angle actuator demonstrate the practical feasibility of this approach.

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 (Plantar PPCD), 其连续动态是确定性、恒定率和平面, 模式之间的离散转换是概率性的, 发生于不易变区域的边界, 而连续状态在切换时不会被重新设定。 这些对平板机器人的细小线性行为模型非常适合。 我们的主要结果是精确的算法, 用于根据各州之间相互可及性和非零概率自滑动的微小假设决定Planar PPCD的绝对性和几乎肯定性稳定性。 我们的主要想法是将Planar PPCD的稳定性问题降低到具有边缘重量的断层时间Markov链上的相应问题。 我们对有错误角度操作器的平板机器人的实验结果证明了这一方法的实际可行性。