Part I: The Frequency Approach to the Mathematical Description of Linear Periodic Objects.-  Discrete Operational Transformations of Functions of Continuous Argument and Operator Description of LTI Systems.- State-Space Analysis of Finite-Dimensional Linear Continuous Periodic (FDLCP) Objects.- Frequency Method in the Theory of FDLCP Objects.- Floquet–Lyapunov Decomposition and its Application.- Part II: PTM approach to SD systems with FDLCP Objects.- Open-Loop SD System with FDLCP Object.- Open-Loop SD System with FDLCP Object and Delay.- Closed-Loop SD System with FDLCP Object and Delay.- Part III: Determinant Polynomial Equations, SD Modal Control and Stabilization of FDLCP Objects.- Polynomial Matrices.- Rational Matrices.- Determinant Polynomial Equations, Causal Modal Control and Stabilization of Discrete Systems.- 11 Synchronous SD Stabilization of FDLCP Objects.- Asynchronous SD Stabilization of FDLCP Objects.- Part IV Building the Quality Functional for the H2-Optimization Task of the System Sτ.- General PTM Properties of Synchronous Open-Loop SD System with Delay.- 14 PTM of the Closed-Loop SD System with Delay as Function of Argument s.- Calculation of Matrices v0(s), ξ0(s), ψ0(s).- System Function.- Representing the PTM of a Closed-Loop Synchronous SD System by the System Function.- H2-Norm of the Closed-Loop SD System.- Construction of the Quality Functional.- Part V H2-Optimization of the Closed-Loop SD System.- Scalar and Matrix Quasi-polynomials.- Minimization of a Quadratic Functional on the Unit Circle.- Construction of Matrix η(s,t).- Construction of Matrix C ̃T (s,t).- Transformation of Quality Functional.- H2-Optimization of the System Sτ.