INVOLUTORY MATRIX DIFFERENTIAL EQUATIONS

Abstract

This chapter discusses involutary matrix differential equations. The interrelations between linear matrix differential systems and associated Riccati matrix differential equations are well known and of frequent use in a variety of instances of variational problems, control theory, and transmission line phenomena. In particular, when the linear system is Hamiltonian and hermitian in nature, there is an intimate connection between such systems and the generalized Sturmian theory. There is a corresponding case wherein the linear differential system is symmetric, but non-real, and in which the basic solvability theorems are strict duals of those in the hermitian case. The discussion is phrased in the context of a generalized differential system that is equivalent to a type of linear vector Riemann–Stieltjes integral equation.