Electrical and Electronic Engineering - Research Publications
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ItemAveraging in singularly perturbed hybrid systems with hybrid boundary layer systems(IEEE, 2012-01-01)We analyze a class of singularly perturbed hybrid systems based on two auxiliary hybrid systems: the averaged system, which approximates the slow dynamics, and the boundary layer system, which approximates the fast dynamics. The average system is generated by averaging the solutions of the boundary layer system. The novelty of this work is that the boundary layer system is a hybrid system rather than a continuous-time system. This extends available results to cover new classes of hybrid systems. We illustrate how to apply our results through an example that is a power converter system under hybrid feedbacks implemented by pulse-width modulation (PWM).
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ItemDiagonal stability for a class of graphs with connected circles(IEEE, 2012)Diagonal stability for a class of matrices having strongly connected graphs is considered, in which each pair of distinct simple circles have at most one common edge or a common vertex. We apply the obtained results to analyze stability of a class of nonlinear dynamical networked systems, for which each subsystem is output strictly passive and the storage function is available. We show that diagonal stability of the dissipativity matrix that includes the information of interconnection structure of subsystems implies that the sum of weighted storage functions is a storage Lyapunov function for this class of networks.
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ItemInput-to-state stability for a class of hybrid dynamical systems via averaging(Springer, 2012-02)Input-to-state stability (ISS) properties for a class of time-varying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the time-varying hybrid systems with time-invariant hybrid systems. Closeness of solutions between the time-varying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semi-global practical (SGP)-ISS of the actual system. In a similar fashion, ISS of the weak average implies semi-global practical derivative ISS (SGP-DISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulse-width modulated control systems.
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ItemAnalysis for a class of singularly perturbed hybrid systems via averaging(PERGAMON-ELSEVIER SCIENCE LTD, 2012-06-01)A class of singularly perturbed hybrid dynamical systems is analyzed. The fast states are restricted to a compact set a priori. The continuous-time boundary layer dynamics produce solutions that are assumed to generate a well-defined average vector field for the slow dynamics. This average, the projection of the jump map in the direction of the slow states, and flow and jump sets from the original dynamics define the reduced, or average, hybrid dynamical system. Assumptions about the average system lead to conclusions about the original, higher-dimensional system. For example, forward pre-completeness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains. In addition, global asymptotic stability for the average system implies semiglobal, practical asymptotic stability for the original system. We give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems. We also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuous-time plants implemented by fast but continuous actuators.
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ItemPath Following for Nonlinear Systems With Unstable Zero Dynamics: An Averaging Solution(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2011-04-01)We consider a path-following problem in which the goal is to ensure that the error between the system output and the geometric path is asymptotically less than a prespecified constant, while guaranteeing a forward motion along the path and boundedness of all states. Comparing with the results on this problem, we exploit averaging techniques to develop an alternative simpler solution for a class of nonlinear systems and for paths satisfying a certain geometric condition.
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ItemInput-to-state stability analysis via averaging for parameterized discrete-time systems(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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ItemInput-to-State Stability and Averaging of Linear Fast Switching Systems(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.