Electrical and Electronic Engineering - Research Publications

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Author: Nesic, Dragan × Author: Wang, Wei × End date: 2010 × Start date: 2009 × Type: Journal Article ×

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    Input-to-state stability analysis via averaging for parameterized discrete-time systems
    Wang, W ; Nešíc, D (Watam Press, 2010-12-15)
    The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly on compact time intervals to the solutions of the average family of discrete-time systems, then ISS of the average family of systems implies SGP-ISS of the original family of systems. A trajectory based approach is utilized to establish the main result.
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    Input-to-State Stability and Averaging of Linear Fast Switching Systems
    Wang, W ; Nesic, D (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-05-01)
    We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in [1], with partial strong average defined in this note, play an important role in the context of switched systems. Using these notions of average, we show that exponential input-to-state stability (ISS) of the strong and the partial strong average system with linear gain imply exponential ISS with linear gain of the actual system. Similarly, exponential ISS of the weak average guarantees an appropriate exponential derivative ISS (DISS) property for the actual system. Moreover, using the Lyapunov method, we show that linear ISS gains of the actual system and its average converge to each other as the switching rate is increased.