Riesz basis generation: Dual-basis approach

This chapter is devoted to the Riesz basis property for wave-like equations. It follows the routs from concrete example to abstract framework. This demonstrates the overall technique. In this chapter, the adjoint basis approach in various situations is introduced, which makes use of the Riesz basis property of exponential families, in particular, the basis property of generalized divided difference (GDD). The chapter starts with two connected strings with span point dissipative feedbacks. An N-connected string system is discussed for its Riesz basis property. The Riesz basis property for an abstract hyperbolic system is also discussed. It also presents three tree-shaped string systems with joint’s feedbacks. The last section discusses the stability of wave equation with delayed output feedback control by the Riesz basis approach.