Mean Escape Time of Switched Riccati Differential Equations

The paper’s Theorem 3.2 derives the coupled renewal equations TA = g1 + M1 TB and TB = g2 + M2 TA for the switched RDE (9), proves that M is a strict contraction with norm bound F(t0) = 1 − e^{−λ t0}, and concludes the Neumann-series solution [TA; TB] = ∑_{k≥0} M^k [g1; g2] via Lemma 1.1 (Neumann series) . The candidate solution reproduces the same first-jump decomposition, the same operator setup on L∞×L∞, the same uniform bound yielding ∥M∥ ≤ 1−e^{−λ t0}, and the same Neumann-series inversion. Apart from notational differences and an explicit bound showing g1, g2 ∈ L∞, the arguments are essentially identical.