We present a general and uni ed framework for the design of nonlinear digital controllers using the emulation method for nonlinear systems with disturbances. It is shown that if a (dynamic) continuous-time controller, which is designed so that the continuous-time closed-loop system satis es a certain dissipation inequality, is appropriately discretized and implemented using sample and zero-order-hold, then the discrete-time model of the closed-loop sampled-data system satis es a similar dissipation inequality in a semiglobal practical sense (sampling period is the parameter that we can adjust). We consider two di erent forms of dissipation inequalities for the discrete-time model: the \weak" form and the \strong" form. The results are also applicable for open-loop systems.

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Abstract-This paper focuses on the refinement of standard Hilbert-Huang transform (HHT) technique to accurately characterize time varying, multicomponents interarea oscillations. Several improved masking techniques for empirical mode decomposition (EMD) and a local Hilbert transformer are proposed and a number of issues regarding their use and interpretation are identified. Simulated response data from a complex power system model are used to assess the efficacy of the proposed techniques for capturing the temporal evolution of critical system modes. It is shown that the combination of the proposed methods result in superior frequency and temporal resolution than other approaches for analyzing complicated nonstationary oscillations.

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used in controller design for a sampled-data system.

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used in controller design for a sampled-data system.