Answer: In the study of engineering control of physical

Chapter 2, Problem 20E

(choose chapter or problem)

Problem 20E

In the study of engineering control of physical systems, a standard set of differential equations is transformed by Laplace transforms into the following system of linear equations:

where A is n × n, B is n × m, C is m × n, and s is a variable. The vector u in ℝm is the “input” to the system, y in ℝm is the “output,” and x in Rn is the “state” vector. (Actually, the vectors x, u, and y are functions of s, but this does not affect the algebraic calculations in Exercises 19 and 20.)

Suppose the transfer function W(s) in Exercise 19 is invertible for some s. It can be shown that the inverse transfer function W(s)–1 which transforms outputs into inputs, is the Schur complement of A – BC – sIn for the matrix below. Find this Schur complement. See Exercise 16.