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Approach-Average

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A N Michel – One of the best experts on this subject based on the ideXlab platform.

  • stability analysis of switched systems with stable and unstable subsystems an average dwell time approach
    International Journal of Systems Science, 2001
    Co-Authors: Guisheng Zhai, Bo Hu, Kazunori Yasuda, A N Michel

    Abstract:

    We study the stability properties of switched systems consisting of both Hurwitz stable and unstable linear time-invariant subsystems using an average dwell time approach. We propose a class of switching laws so that the entire switched system is exponentially stable with a desired stability margin. In the switching laws, the average dwell time is required to be sufficiently large, and the total activation time ratio between Hurwitz stable subsystems and unstable subsystems is required to be no less than a specified constant. We also apply the result to perturbed switched systems where nonlinear vanishing or non-vanishing norm-bounded perturbations exist in the subsystems, and we show quantitatively that, when norms of the perturbations are small, the solutions of the switched systems converge to the origin exponentially under the same switching laws.

  • stability analysis of switched systems with stable and unstable subsystems an average dwell time approach
    American Control Conference, 2000
    Co-Authors: Guisheng Zhai, Bo Hu, Kazunori Yasuda, A N Michel

    Abstract:

    We study the stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems using an average dwell time approach. We show that if the average dwell time is chosen sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of Hurwitz stable subsystems, then exponential stability of a desired degree is guaranteed. We also derive a piecewise Lyapunov function for the switched system subjected to the switching law and the average dwell time scheme under consideration, and we extend these results to the case for which nonlinear norm-bounded perturbations exist in the subsystems. We show that when the norms of the perturbations are small, we can modify the switching law appropriately to guarantee that the solutions of the switched system converge to the origin exponentially with large average dwell time.

Douglas P Hanel – One of the best experts on this subject based on the ideXlab platform.

  • use of a distraction plate for distal radial fractures with metaphyseal and diaphyseal comminution surgical technique
    Journal of Bone and Joint Surgery American Volume, 2006
    Co-Authors: T Ginn, David S Ruch, Charles Yang, Douglas P Hanel

    Abstract:

    BACKGROUND: Distal radial fractures with extensive comminution involving the metaphyseal-diaphyseal junction present a major treatment dilemma. Of particular difficulty are those fractures involving the articular surface. One approach is to apply a dorsal 3.5-mm plate extra-articularly from the radius to the third metacarpal, stabilizing the diaphysis and maintaining distraction across the radiocarpal joint. METHODS: Twenty-two patients treated with a distraction plate for a comminuted distal radial fracture were included in the study. With use of three limited incisions, a 3.5-mm ASIF plate was applied in distraction dorsally from the radial diaphysis, bypassing the comminuted segment, to the long-finger metacarpal, where it was fixed distally. The articular surface was anatomically reduced and was secured with Kirschner wires or screws. Eleven of the twenty-two fractures were treated with bone-grafting. The plate was removed after fracture consolidation (at an average of 124 days), and wrist motion was initiated. All patients were followed prospectively with use of radiographs, physical examination, and DASH (Disabilities of the Arm, Shoulder and Hand) scores. RESULTS: All fractures united by an average of 110 days. Radiographs showed an average palmar tilt of 4.6 degrees and an average ulnar variance of neutral (0 degrees), whereas loss of radial length averaged 2 mm. Flexion and extension averaged 57 degrees and 65 degrees, respectively, and pronation and supination averaged 77 degrees and 76 degrees, respectively. The average DASH scores were 34 points at six months, 15 points at one year, and 11.5 points at the time of final follow-up (at an average of 24.8 months). According to the Gartland-Werley rating system, fourteen patients had an excellent result, six had a good result, and two had a fair result. Grip strength and the range of motion of the wrist at one year correlated inversely with the proximal extent of fracture comminution into the diaphysis. The duration of plate immobilization did not correlate with the range of motion of the wrist or with the DASH score at one year. CONCLUSIONS: The use of a distraction plate combined with reduction of the articular surface and bone-grafting when needed can be an effective technique for treatment of fractures of the distal end of the radius with extensive metaphyseal and diaphyseal comminution. A functional range of motion with minimal disability can be achieved despite a prolonged period of fixation with a distraction plate across the wrist joint.

  • use of a distraction plate for distal radial fractures with metaphyseal and diaphyseal comminution
    Journal of Bone and Joint Surgery American Volume, 2005
    Co-Authors: David S Ruch, Adam T Ginn, Charles Yang, Beth P Smith, Julia Rushing, Douglas P Hanel

    Abstract:

    BACKGROUND: Distal radial fractures with extensive comminution involving the metaphyseal-diaphyseal junction present a major treatment dilemma. Of particular difficulty are those fractures involving the articular surface. One approach is to apply a dorsal 3.5-mm plate extra-articularly from the radius to the third metacarpal, stabilizing the diaphysis and maintaining distraction across the radiocarpal joint.

    METHODS: Twenty-two patients treated with a distraction plate for a comminuted distal radial fracture were included in the study. With use of three limited incisions, a 3.5-mm ASIF plate was applied in distraction dorsally from the radial diaphysis, bypassing the comminuted segment, to the long-finger metacarpal, where it was fixed distally. The articular surface was anatomically reduced and was secured with Kirschner wires or screws. Eleven of the twenty-two fractures were treated with bone-grafting. The plate was removed after fracture consolidation (at an average of 124 days), and wrist motion was initiated. All patients were followed prospectively with use of radiographs, physical examination, and DASH (Disabilities of the Arm, Shoulder and Hand) scores.

    RESULTS: All fractures united by an average of 110 days. Radiographs showed an average palmar tilt of 4.6° and an average ulnar variance of neutral (0°), whereas loss of radial length averaged 2 mm. Flexion and extension averaged 57° and 65°, respectively, and pronation and supination averaged 77° and 76°, respectively. The average DASH scores were 34 points at six months, 15 points at one year, and 11.5 points at the time of final follow-up (at an average of 24.8 months). According to the Gartland-Werley rating system, fourteen patients had an excellent result, six had a good result, and two had a fair result. Grip strength and the range of motion of the wrist at one year correlated inversely with the proximal extent of fracture comminution into the diaphysis. The duration of plate immobilization did not correlate with the range of motion of the wrist or with the DASH score at one year.

    CONCLUSIONS: The use of a distraction plate combined with reduction of the articular surface and bone-grafting when needed can be an effective technique for treatment of fractures of the distal end of the radius with extensive metaphyseal and diaphyseal comminution. A functional range of motion with minimal disability can be achieved despite a prolonged period of fixation with a distraction plate across the wrist joint.

Philip H. Stauffer – One of the best experts on this subject based on the ideXlab platform.

  • On estimating functional average breakthrough curve using time‐warping technique and perturbation approach
    Water Resources Research, 2012
    Co-Authors: Zhiming Lu, Philip H. Stauffer

    Abstract:

    [1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the arithmetic average of all realizations. The arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the arithmetic average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional average is the percentile average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and arithmetic average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.

  • on estimating functional average breakthrough curve using time warping technique and perturbation approach
    Water Resources Research, 2012
    Co-Authors: Zhiming Lu, Philip H. Stauffer

    Abstract:

    [1] Simulated contaminant breakthrough curves (BTC) are often used to predict mass arrival at compliance boundaries at waste storage sites. In numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties, Monte Carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the arithmetic average of all realizations. The arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate. The averaged breakthrough curve usually does not resemble any of individual breakthrough curves. The reason is that BTCs vary not only on amplitude but also on dynamics (time) and therefore it is not appropriate to take the arithmetic average directly. In this study, we consider each BTC as a random curve, and use time-warping techniques to align all curves in a time-warped space, compute the sample mean of the curves in the time-warped space, and transform the means back to the original time space. We show that all BTCs are aligned based on the percentile of mass reaching the compliance boundary, and the functional average is the percentile average of all BTCs. The confidence interval of the sample mean curve is estimated using the perturbation approach. The functional average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and arithmetic average curves. The method is illustrated using transport simulations at the Material Disposal Area G, Los Alamos National Laboratory (LANL) in New Mexico.