ABSTRACT
Inmany applications, such as diffusion and structural vibrations, the physical quantity of interest depends on both position and time. Some examples are shown in Figures 67.1 through 67.3. These systems are modeled by partial differential equations (PDEs) and the solution evolves on an infinite-dimensional Hilbert space. For this reason, these systems are often called infinite-dimensional systems. In contrast, the state of a systemmodeled by an ordinary differential equation evolves on a finite-dimensional system, such as Rn, and these systems are called finite-dimensional. Since the solution of the PDE reflects the distribution in space of a physical quantity such as the temperature of a rod or the deflection of a beam, these systems are often also called distributed-parameter systems (DPS). Systemsmodeled by delay differential equations also have a solution that evolves on an infinite-dimensional space. Thus, although the physical situations are quite different, the theory and controller design approach is quite similar to that of systems modeled by PDEs. However, delay differential equations will not be discussed directly in this chapter.
