"A spectral criterion for the existence of the stabilizing solution of a class of Riccati type differential equations with periodic coefficients"

"In this paper, we investigate the existence and uniqueness of a stabilizing solution to a periodic backward nonlinear differential equation. This class of nonlinear equations includes as special cases many of the continuous-time Riccati equations arising both in deterministic and stochastic linear quadratic (LQ) type control problems."

An efficient procedure to speed up critical plane search in multiaxial fatigue: Application to the Carpinteri-Spagnoli spectral criterion

A more efficient procedure is proposed to speed up the Carpinteri-Spagnoli (CS) algorithm in numerical computations. The goal is accomplished by deriving the exact solution for the spectral moments and expected maximum peak of normal/shear stress in any rotated plane orientation. The algorithm then avoid the use of “for/end” loops to identify the five rotations that locate the critical plane in CS method. The procedure is especially advantageous if applied to three-dimensional finite element analysis, in which the stress spectra in thousands of nodes need to be processed iteratively. The procedure is based on theoretical results that have, however, a more general validity, being applicable to any multiaxial criterion that makes use of angular rotations to identify the critical plane.

IMPROVEMENT AND EXTENSION OF SHAPE EVALUATION CRITERIA IN MULTI-SCALE IMAGE SEGMENTATION

From the last decade, the multi-scale image segmentation is getting a particular interest and practically being used for object-based image analysis. In this study, we have addressed the issues on multi-scale image segmentation, especially, in improving the performances for validity of merging and variety of derived region’s shape. Firstly, we have introduced constraints on the application of spectral criterion which could suppress excessive merging between dissimilar regions. Secondly, we have extended the evaluation for <i>smoothness</i> criterion by modifying the definition on the extent of the object, which was brought for controlling the shape’s diversity. Thirdly, we have developed new shape criterion called <i>aspect ratio</i>. This criterion helps to improve the reproducibility on the shape of object to be matched to the actual objectives of interest. This criterion provides constraint on the aspect ratio in the bounding box of object by keeping properties controlled with conventional shape criteria. These improvements and extensions lead to more accurate, flexible, and diverse segmentation results according to the shape characteristics of the target of interest. Furthermore, we also investigated a technique for quantitative and automatic parameterization in multi-scale image segmentation. This approach is achieved by comparing segmentation result with training area specified in advance by considering the maximization of the average area in derived objects or satisfying the evaluation index called F-measure. Thus, it has been possible to automate the parameterization that suited the objectives especially in the view point of shape’s reproducibility.

IMPROVEMENT AND EXTENSION OF SHAPE EVALUATION CRITERIA IN MULTI-SCALE IMAGE SEGMENTATION

From the last decade, the multi-scale image segmentation is getting a particular interest and practically being used for object-based image analysis. In this study, we have addressed the issues on multi-scale image segmentation, especially, in improving the performances for validity of merging and variety of derived region’s shape. Firstly, we have introduced constraints on the application of spectral criterion which could suppress excessive merging between dissimilar regions. Secondly, we have extended the evaluation for &lt;i&gt;smoothness&lt;/i&gt; criterion by modifying the definition on the extent of the object, which was brought for controlling the shape’s diversity. Thirdly, we have developed new shape criterion called &lt;i&gt;aspect ratio&lt;/i&gt;. This criterion helps to improve the reproducibility on the shape of object to be matched to the actual objectives of interest. This criterion provides constraint on the aspect ratio in the bounding box of object by keeping properties controlled with conventional shape criteria. These improvements and extensions lead to more accurate, flexible, and diverse segmentation results according to the shape characteristics of the target of interest. Furthermore, we also investigated a technique for quantitative and automatic parameterization in multi-scale image segmentation. This approach is achieved by comparing segmentation result with training area specified in advance by considering the maximization of the average area in derived objects or satisfying the evaluation index called F-measure. Thus, it has been possible to automate the parameterization that suited the objectives especially in the view point of shape’s reproducibility.

H2/H∞Control Design of Detectable Periodic Markov Jump Systems

An infinite horizonH2/H∞control problem is addressed for discrete-time periodic Markov jump systems with(x,u,v)-dependent noise. Above all, by use of the spectral criterion of detectability, an extended Lyapunov stability theorem is developed for the concerned dynamics. Further, based on a game theoretic approach, a state-feedbackH2/H∞control design is proposed. It is shown that under the condition of detectabilityH2/H∞feedback gain can be constructed through the solution of a group of coupled periodic difference equations.