Stability Analysis of Planar Probabilistic Piecewise Constant Derivative Systems
This work addresses stability analysis for planar robots modeled as stochastic hybrid systems, but it appears incremental as it focuses on a specific subclass with probabilistic switching.
The paper tackles the problem of stability analysis for a subclass of stochastic hybrid systems called Planar Probabilistic Piecewise Constant Derivative Systems, which model planar robots, and presents an exact algorithm for deciding absolute and almost sure stability under mild assumptions.
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.