# Riesz Basis Generation: Green Function Approach

Chapter
Part of the Communications and Control Engineering book series (CCE)

## Abstract

In this chapter, we discuss another approach for Riesz basis the so-called Green function approach. This happens for beam equations where the boundary feedback control is of the same order as the original but we cannot apply the approach in Chapter 4 for this situation because the exponential family is usually not Riesz basis for the spectrum not being the strip paralleling to the imaginary axis. It starts with a rotating beam with shear force feedback. The system is not dissipative in the traditional sense. Section 5.2 discusses the beam equation with the conjugate variables appearing at the same boundary. The Green function method is applied to develop the Riesz basis property and the well-posedness of the system is concluded as a consequence. Section 5.3 presents a one-link flexible manipulator with rotational inertia.

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