ABSTRACT
The first step in system analysis is the determination of process characteristics such as stability and transient response. This chapter focuses on analytical techniques that do not require the solution of a model and hence offer the possibility of a generic account of process stability. Specifically, it is shown that that the stability of a linear dynamic process is captured by the eigenvalues of its state matrix which are equivalent to the poles of the corresponding transfer function model. To declare the process to be stable, the real parts of all the eigenvalues of the state matrix would lie in the left half of the complex plane. Three methods are introduced for stability analysis. In Routh's criterion, the goal is to determine the stability condition (stable or unstable) of a system without actually computing the poles of the transfer function model. In Root-Locus analysis, the roots of the characteristic function are traced in the complex plane as a function of a system parameter, thus providing insight toward the extent of stability. The direct substitution method takes advantage of the complex plane and evaluates the roots of the characteristic equation at the imaginary axis.
