ABSTRACT
Themotivation for this chapter is to present mathematical tools for analysis and design of open-and closed-loop continuous-and discrete-time control systems. A broad class of linear time-invariant (LTI) systems can be represented by linear differential equations (DEs) with constant coefficients in case of continuous-time and linear difference equations with constant coefficients in case of discrete-time systems. The Fourier and Laplace transforms play important roles in analyzing and designing such systems. The z-transform is a tool for analyzing and designing discrete-time systems and is the counterpart of Laplace transform that is used for continuous-time systems. In this chapter, we introduce LTI continuous-time systems, Laplace transform, discrete-time systems, and z-transform. Matrices and linear algebra are also important tools in analyzing control systems in the state-space form. Eigenvalues and eigenvectors, singular value decomposition (SVD), and functions of matrices are other mathematical tools used to design control systems with state-space approach. The rest of this chapter is devoted to this important subject.
