ABSTRACT
Matrix polynomials and functions of matrices have extensive applications in different engineering problems such as modern control system design, vibration analysis, queueing theory, and communication systems. This chapter focuses on matrix polynomials, special functions of square matrices and discusses their analytical and numerical computation. There are several techniques available to find a function of a matrix. They include: use of Sylvester theorem, Cayley-Hamilton technique, and matrix diagonalization. Conventional control system design is rooted in transfer function and frequency response analysis. Modern control theory, on the other hand, is based on the state space formulation of the system. One advantage of modern control theory over the conventional approach is in its applicability to both single-input single-output and multiple-input multiple-output systems. The chapter presents the fundamentals of system modeling in state space, the solutions of state equations, and the determination of controllability and observability of linear time invariant systems for both continuous as well as discrete-time systems.
