Modified Bilinear Integration Algorithm Based on the Modulated Sine Function

This study presents a novel discretization method for converting an analogue controller into its corresponding counterpart for a discrete-time system. The proposed method is appropriate for the natural response curve and, thus, is more effective for certain digitally redesigned systems. Based on the mapping region of the transformation using the proposed method from the s-domain to the z-domain, a transformation involving a modulated parameter n is used to generate a corresponding stable discrete-time controller for a stable continuous-time controller. As a suitable modulated parameter in the proposed transformation is selected to digitalize an analogue-controlled system, the new sampled-data-controlled system achieves a precise discrete-time response, and can also tolerate a large sampling period for sample-data implementation. A simulated example is used to demonstrate the results.

Bilinear integration with positive vector measures

The integration of vector (and operator) valued functions with respect to vector (and operator) valued measures can be simplified by assuming that the measures involved take values in the positive elements of a Banach lattice.

Joint continuity of injective tensor products of vector measures in Banach lattices

It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle's bilinear integration theory.