ABSTRACT
This chapter presents certain mathematical topics necessary for the study of control systems, and offers the appropriate mathematical background on subjects such as basic control signals, Laplace transform, and the theory of matrices. It presents definitions of the following basic control signals: the step function, the gate function, the impulse function, the ramp function, the exponential function, and the sinusoidal function. To study and design control systems, one relies to a great extent on a set of mathematical tools. A popular application of the Laplace transform is in solving linear differential equations with constant coefficients. In this case, the motivation for using the Laplace transform is to simplify the solution of the differential equation. The Laplace transform is a mathematical tool which transforms a function from one domain to another. In particular, it transforms a time-domain function to a function in the frequency domain and vice versa.
