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Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions 认领 引用
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作者 Pan Xiong Feng Wang +1 位作者 Xibin Cao Guangren Duan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2013年第6期984-991,共8页
The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst... The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances. 展开更多
关键词 linear uncertain system robust D-stability analysis linear matrix inequality （LMI） condition affine parameterdependent Lyapunov function matrix polytope.
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An Alternative for Time Series Models 认领 引用
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作者 Jerzy Filus 《China-USA Business Review》 2014年第5期297-304,共8页
Two methods for construction of new stochastic processes with discrete time are presented. One of the methods employs as the defining tool “triangular （more specifically ＇pseudoaffine＇） transformations” which ar... Two methods for construction of new stochastic processes with discrete time are presented. One of the methods employs as the defining tool “triangular （more specifically ＇pseudoaffine＇） transformations” which are extended from the Euclidean R^n to infinite dimension space. They transform any well-known discrete time stochastic process into the constructed one. The other more flexible method is the “method of parameter dependence”, extended to infinite dimension. Properties of the obtained stochastic processes （by either method） indicate the possibility to apply them for financial analysis, as an alternative for the classical time series models. The advantage of the presented models over the existing ones first of all relies on expected better accuracy. This follows from the fact that the typically held assumption on Markovianity in the existing models can easily be relaxed. The defined processes may incorporate a quite long memory including, among others, the k-Markovian cases for k _〉 2. Regardless the non-Markovianity of the models they still are tractable in an analytical or numerical way. The stochastic processes defined in this paper provide more flexible and more general tools than the existing time series models for modeling financial problems. Among others, they make it possible to incorporate the influence of environmental （explanatory） random variables on the underlying stochastic models＇ behavior. These additional features turn out to be describable by the method of parameter dependence. Some suggestions for an associated preliminary statistical analysis are included. 展开更多
关键词 stochastic dependence stochastic processes alternative for time series financial models parameterdependence method of construction k-Markovianity
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