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

Authors:
John M. Davis;Johnny Henderson;K. Rajendra Prasad
Affiliations:
Department of Mathematics, Baylor University, Waco, TX;Department of Mathematics, Auburn University, Auburn, AL;Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003 India
Venue:
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Year:
2002

Citing 3
Cited 0

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Abstract

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.