  Riccati differential equations is the class of first-order and quadratic
ordinary differential equations and has various applications in the systems and
control theory. In this paper, we analyze a switched Riccati differential
equation that is driven by a Poisson-like stochastic signal. We specifically
focus on the computation of the mean escape time of the switched Riccati
differential equation. The contribution of this paper is twofold. We first show
that, under the assumption that the subsystems described as a deterministic
Riccati differential equation escape in finite time regardless of its initial
state, the mean escape time of the switched Riccati differential equation
admits a power series expression. In order to further expand the applicability
of this result, we then present an approximative formula for computing the
escape time of deterministic Riccati differential equations. We present
numerical simulations to illustrate the obtained results.
