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This paper aims at the H∞ fixed-interval smoothing problem for linear continuous-time systems with l + 1 time-delay observations. Such problem will be converted into H2 fixed-interval smoothing problem for linear time-delay systems in indefinite space. Therefore, the H∞ fixed-interval smoothing problem is solved by using the orthogonal projection theory in indefinite space, and the fixed-interval...
In this paper, we discuss the moment problem of g-frames in Hilbert spaces. Firstly, we give the definition of moment problem which is based on operators, and discuss the necessary and sufficient conditions of the existence of its solution. Secondly, we discuss its best approximative solution by orthogonal projection when it has no exact solution.
A complex domain projection method of analysis is proposed based on the transient representation of electro-magnetic traveling wave (EM) for transmission line. Considering the impact of distributed parameters and the characteristics of electro-magnetic wave, the transmission line model is built. The instantaneous voltage equation and the fault location function are derived and obtained and the former...
This paper introduces an index which can be used as a measure of correlation between features of a multidimensional feature vector. The proposed index has been intuitively explained using constant distance loci of Mahalanobis metric. More rigorous explanation has been given using orthogonal decomposition of the vector space. The application of the proposed index has been given using 2D synthetic data.
Based on orthogonal projection, a non-interior point continuation algorithm for second-order cone programming problems is proposed and analyzed. The main idea of the method is that we reformulate the complementary condition in the optimality conditions as a projection equation. Using this reformulation, we only need to solve a system of linear equations, compute two simple projections and perform...
This paper deals with subspace-based identification of unstable systems. Because the system is unstable, we will assume the experimental data are generated under stabilizing feedback. In order to remove the effect of noise an orthogonal projection is used. The system state space matrices are recovered from the extended observability matrix. The subspace-based identification algorithm is tested on...
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