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As the emissions and fuel economy standards for internal combustion engines become ever more stringent, a variety of valvetrain control methods have been developed to improve engine performance. One of these is camshaft (CAM) phasing, which controls the angular position of the CAM relative to the crankshaft allowing changes to the timing of valve lift events. This method has demonstrated advantages including broadening the engine torque curve, increasing peak power at higher RPM, reducing hydrocarbon and NOx emissions, and improving fuel economy. In addition, external EGR systems can be eliminated because internal cylinder dilution control can be achieved by varying CAM timing. Current implementations of CAM phasing use oil-pressure-based electro-mechanical systems. While these systems are relatively low cost and have proven to be robust, they have disadvantages at low oil temperatures and pressures (such as during cranking events).

Stability is an essential indicator of proper system operation. To this end, it is often of interest to predict the Region of Asymptotic Stability (RAS) associated with an equilibrium point of interest. In the case of the presence of constraints that need to be satisfied, one is faced with the problem of estimating a Restricted RAS (RRAS). Practical methods for estimating RRASs have been proposed and demonstrated for relatively high-order systems. These methods are based on Lyapunov's second method. However, they do not address the problem of constructing an optimal Lyapunov function. In this paper, a method of finding a Lyapunov function that yields improved estimates of the restricted region of asymptotic stability is set forth. In addition, a new method for estimating RRASs based on the average of the Lyapunov derivative is also set forth. Numerical examples illustrate the utility of the proposed methods.

A complete system approach to power semiconductor analysis and selection is set forth in this paper. In order to address design overkill, a suitable power profile across the desired drive schedule is obtained through vehicle simulation in lieu of worse case operating conditions. The representative profile is then applied to detailed models of the inverter, power device, and power device thermal stack-up in order to predict worse case, silicon junction temperature rise. The simulation stream includes a closed silicon thermal loop that leads to more accurate power loss and junction temperature calculations. The models are combined and exercised in a single platform for ease of integration and fast simulation. Herein, the methods will be applied to a working example of an inverter for motor drives, and analytical results will be reviewed.