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Motivated by the need to simultaneously guarantee safety and stability of safety-critical dynamical systems, we construct permissive barrier certificates in this paper that explicitly maximize the region where the system can be stabilized without violating safety constraints. An optimization strategy is developed to search for the maximum volume barrier certified region of safe stabilization. The barrier certified region, which is allowed to take any arbitrary shape, is proved to be strictly larger than safe regions generated with Lyapunov sublevel set based methods. The proposed approach effectively unites a Lyapunov function with multiple barrier functions that might not be compatible with each other. Iterative search algorithms are developed using sum-of-squares to compute the most permissive, that is, the maximum volume, barrier certificates. Simulation results of the iterative search algorithm demonstrate the effectiveness of the proposed method.

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Abstract-Robust synchronization problem is a key issue in chaotic circuits and nonlinear systems. This paper is concerned with robust synchronization problem of polynomial nonlinear system affected by time-varying uncertainties on topology, i.e., structured uncertain parameters constrained in a boundedrate polytope. Via partial contraction analysis, novel conditions, both for robust exponential synchronization and for robust asymptotical synchronization, are proposed by using parameterdependent contraction matrices. In addition, for polynomial nonlinear system, this paper introduces a new class of contraction matrix, i.e., homogeneous parameter-dependent polynomial contraction matrix (HPD-PCM), by which tractable conditions of linear matrix inequalities (LMIs) are provided via affine space parametrizations. Furthermore, the variant rate margin for robust asymptotical synchronization is, for the first time, proposed and investigated via handling generalized eigenvalue problems (GEVPs). A set of representative examples demonstrate the effectiveness of proposed method.

A study of high-efficiency premixed low-temperature combustion (LTC) with dieseline (a blend of diesel and gasoline) was conducted on a high-speed compression ignition engine and strategies to broaden the operational range of this dieseline LTC were investigated. Increased ignition delay and higher volatility of dieseline relative to diesel fuel contribute to produce a well-mixed charge, and a simultaneous reduction in NO x and smoke emissions with a moderate exhaust gas recirculation (EGR) rate can be achieved across a relatively narrow load window. An intake boost strategy was employed to broaden the LTC operational window. Higher intake pressure increases air charge and allows for higher fuelling, so the upper load limit of this LTC mode is extended. An increase in NO x emissions is observed at light to mid loads, but a slight increase in EGR rate can reduce NO x emissions to an acceptable level. Because dieseline requires only a relatively light use of EGR, combustion efficiency across the entire dieseline LTC operational range is maintained at a high level.

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