Upper and lower bounds for the solution of the general matrix Riccati differential equation on a time scale

We obtain upper and lower bounds for the solution of the general matrix Riccati differential equation on a time scale T,RΔ(t)=A(t)+B(t)R(t)+R(σ(t))B∗(t)−R(σ(t))C(t)R(t),where A(t) and C(t) are symmetric n×n matrices while B(t), V(t), T(t), and R(t) are n×n matrices, and ∗ denotes the transpose of the matrix. We use the quasilinearization technique to obtain these bounds. We also study the monotonicity of the successive approximations.