I. Introduction

Dynamical systems can be described by differential equations, whose order depends upon the process complexity, coupling between the subsystems, and on the degree of accuracy required for the specific application. The state space representation transforms higher-order differential equations into a set of coupled first-order equations. The two important issues that characterize the postulated model are 1) choice of the state variables and 2) input output and internal system behavior. The set of states which can be chosen to represent a system is never unique, but will depend upon the pertinent physical characteristics of the system being modeled. Having selected appropriate states, the internal system behavior is then characterized by the system parameters. Such models in terms of states and parameters for real-world processes are mostly nonlinear. Linear system models are simplified representations of nonlinear processes. They are obtained through linearization about a pre-defined operating point, and hence are valid for small variations around the point of linearization.

Having postulated a model, it becomes possible to investigate the time propagation of states through simulation, usually by solving an initial-value problem applying numerical integration procedures. The model responses are composed of different modes, some of which may be fast decaying and others slow, requiring longer oscillation time. For stiff systems, that is, when two modes characterized by the smallest and the largest eigenvalues differ greatly, special integration algorithms are necessary. The fidelity of simulated model responses is determined by comparing them with the measured system outputs. Because measurements are likely to...