Chang transformation for decoupling of singularly perturbed linear slowly time-varying systems

Chang transformation is a decoupling technique for singularly perturbed linear systems. However, for linear slowly time-varying systems, construction of the transformation requires solutions of Differential Riccati Equation (DRE) and Differential Sylvester Equations (DSE). In this paper, through the construction of a contraction mapping for the remainders R_L and R_H, Theorem 1 provides iterative solutions in an interval of the singular perturbation parameter ε for the DRE and DSE, which are key steps for Chang transformation construction. Based on the iterative solutions, the concepts of pth-order approximated Chang transformation, decoupled system, pth-order approximated slow and fast systems are established, thereby facilitating the analysis in subsequent investigation on estimate of the Singular Perturbation Margin (SPM) for Linear Slowly Time-Varying systems and Nonlinear Slowly Time-Varying systems.