Mean escape time of switched Riccati differential equations

Riccati differential equations are a class of first-order quadratic ordinary differential equations and have various applications in systems and control theory. In this study, we analyzed a switched Riccati differential equation driven by a Poisson-like stochastic signal. We specifically focused on computing the mean escape time of the switched Riccati differential equation. The contribution of this study is twofold. We first show that, under the assumption that the subsystems described as deterministic Riccati differential equations escape in finite time regardless of their initial state, the mean escape time of the switched Riccati differential equation admits a power series expression. To further expand the applicability of this result, we then present an approximate formula to compute the escape time of deterministic Riccati differential equations. Numerical simulations were performed to illustrate the obtained results.& COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

In this study, we analyzed a switched Riccati differential equation driven by a Poisson-like stochastic signal and focused on computing the mean escape time. We found that the mean escape time of the switched Riccati differential equation has a power series expression under the assumption that the subsystems described as deterministic Riccati differential equations escape in finite time regardless of their initial state. Additionally, we presented an approximate formula to compute the escape time of deterministic Riccati differential equations and demonstrated the obtained results through numerical simulations.