Abstract
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 e 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.
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