Intro; Preface; Contents; Abstract; 1 Preliminaries; 1.1 Normed Linear Spaces; 1.2 Linear Operators on Banach Spaces; 1.3 C0-Semigroups; 1.4 Sobolev Spaces; References; 2 Bases in Hilbert Spaces; 2.1 Riesz Basis; 2.2 Perturbation of Riesz Bases; 2.3 Entire Functions of Exponential Type; 2.4 Pavlov Theorem; 2.5 Functions of Sine Type; 2.6 Generalized Divided Difference (GDD) and Riesz Basis in Parenthesise; 2.7 Riesz Spectral Operator; 2.8 D-Type Operator; 2.9 One-Rank Perturbation for D-Type Operator; 2.10 Riesz Basis for C0-Semigroup; 2.10.1 Riesz Basis for Discrete Operator

2.10.2 Keldysh TheoremReferences; 3 Riesz Basis Generation: Comparison Method; 3.1 Boundary Stabilization for Euler-Bernoulli Beam; 3.2 Boundary Stabilization with a Tip Mass; 3.3 Euler-Bernoulli Beam with Variable Coefficients; 3.3.1 Beam Equation with Variable Coefficients; 3.3.2 Beam Equation with Variable Viscous Damping; 3.4 Boundary Control of a Hybrid System; 3.4.1 Spectral Analysis; 3.4.2 Riesz Basis Generation; 3.4.3 Exponential Stability; 3.4.4 Exact Controllability; 3.5 Connected Beam with Joint Feedback Control; 3.5.1 The Asymptotic Expansion of Eigenvalues

3.5.2 Asymptotic Expansion of Eigenfunctions and Riesz Basis Generation3.6 Thermoelastic System; 3.6.1 Asymptotic Distribution of Eigenvalues; 3.6.2 Asymptotic Expansion of Eigenfunctions; 3.7 Wave Equation with Boltzmann Damping; 3.7.1 Infinite Memory: System Operator Setup; 3.7.2 Infinite Memory: Spectral Analysis; 3.7.3 Finite Memory: System Operator Setup; 3.7.4 Finite Memory: Spectrum of System Operator; 3.7.5 Riesz Basis Property; References; 4 Riesz Basis Generation: Dual-Basis Approach; 4.1 Coupled String; 4.1.1 Riesz Basis Property; 4.1.2 Stability

4.2 N-connected Wave Equation with Joint Feedbacks4.3 Hyperbolic System with Static Boundary Condition; 4.4 Connected Rayleigh Beams; 4.4.1 Riesz Basis Property; 4.4.2 Stability; 4.5 Tree-Shaped Beam Network; 4.5.1 Asymptotic Behavior of Eigenfrequencies; 4.5.2 Riesz Basis Property; 4.6 Wave Equation with Long-Time Delay; 4.6.1 Riesz Basis Property; 4.6.2 Exponential Stability; 4.6.3 Convergence of the Stability Region; 4.6.4 Lack of Robustness to a Small Perturbation in Time Delay; References; 5 Riesz Basis Generation: Green Function Approach; 5.1 A Rotating Beam with Shear Force Feedback

5.1.1 Asymptotic Expansion of Eigenpairs5.1.2 Completeness of the Root Subspace; 5.1.3 Riesz Basis Generation; 5.2 Conjugate Variables Appearing at the Same Boundary; 5.2.1 Asymptotic Analysis for Eigenpairs; 5.2.2 Riesz Basis Property; 5.3 Abstract Second-Order System with General Non-separated Boundary Conditions; 5.3.1 Preliminaries; 5.3.2 Spectral Analysis and Completeness of Root Subspace; 5.3.3 Riesz Basis Generation; 5.3.4 Application to Noncollocated Vibration Control; References; 6 Stabilization of Coupled Systems Through Boundary Connection; 6.1 Beam and Heat Coupling System