Halanay A., Samuel J. Differential Equations, Discrete Systems and Control

Amsterdam: Springer, 1997. - 360p.
This volume presents some of the most important mathematical tools for studying economic models. It contains basic topics concerning linear differential equations and linear discrete-time systems; a sketch of the general theory of nonlinear systems and the stability of equilibria; an introduction to numerical methods for differential equations, and some applications to the solution of nonlinear equations and static optimization. The second part of the book discusses stabilization problems, including optimal stabilization, linear-quadratic optimization and other problems of dynamic optimization, including a proof of the Maximum Principle for general optimal control problems. All these mathematical subjects are illustrated with detailed discussions of economic models.Linear and Affine Differential Equations. Equations with Separated Variables.
Linear Differential Equations with Constant Coefficients.
Linear Systems with Constant Coefficients.
General Theory of Nonlinear Systems. Stability.
Numerical Solution of Differential Equations.
Control Systems. Stabilization of Linear Systems.
Optimal Stabilization.
Linear-Quadratic Optimization on Finite Horizon.
Some Unconstrained Dynamic Optimization Problems.
General Problem of Optimal Control.