Introduction to System Science with MATLAB, 2nd Edition

5Multiple‐Input Systems

Most real, rational systems are influenced and affected by many inputs or causes and, although it is generally possible to reduce or combine these inputs into a single dominant input, there are situations where multiple system inputs must be considered. In this chapter, we will examine in detail the analysis of multiple‐input systems based on analytical methods available for a given system kernel. Although we will find that we are able to obtain analytical solutions for only a limited class of the possible continuous multiple‐input system equations, through the general requirement for “exactness of a given total differential equation,” we will be able to determine whether a given system equation is integrable with a solution of the form

for the multiple‐input c and single‐output e. This exactness test will eliminate unproductive searches and attempts at finding closed, analytical solutions for systems that do not have that solution form.

5.1 Definition and Mathematical Significance

Multiple‐input system models are applicable to any system where it is necessary to assume that more than one significant input is required to adequately describe the system’s output response. Although most systems are influenced by many inputs, it is usually desirable to minimize the number of these inputs to simplify the resulting system equations and reduce the analysis ...