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New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovski\u{i} functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies., Comment: The work is the full version of the paper https://doi.org/10.1016/j.automatica.2020.109227

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many existing inequalities in the published literature, including those with free matrix variables, are the special cases of our inequalities. An relation on the lower bounds of the proposed inequalities is also established. For specific applications, our inequalities are applied to construct a Liapunov-Krasovskii functional for the stability analysis of a linear coupled differential-difference system with a distributed delay, which gives to equivalent stability conditions based on the properties of the proposed inequalities. Finally, it is worthy to note that the inequalities in this note can be applied in general contexts such as the stability analysis of PDE-related systems or sampled-data systems.

This paper develops a novel power harvesting system to harvest ambient RF energy to power a wireless sensor. Harvesting ambient RF energy is a very difficult task as the power levels are extremely weak. Simulation results show zero threshold MOSFETs are essential in the RF to DC conversion process. 0.5VDC at the output of the RF to DC conversion stage is the minimum voltage which must be achieved for the micro-power sensor circuitry to operate. The weakest power level the proposed system can successfully harvest is -37dBm. The measured available power from the FM band has been measured to fluctuate between -33 to -43dBm using a ribbon FM dipole antenna. Ambient RF energy would best be used in conjunction with other forms of harvested ambient energy to increase diversity and dependability. The potential economic and environmental benefits make such endeavors truly worthwhile.