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Smith Form of Triangular Multivariate Polynomial Matrix

Journal of systems Science & Complexity 2023年第1期36卷 151-164页

作者： LIU Jinwang WU Tao LI Dongmei School of Mathematics and Computing Sciences Hunan University of Science and TechnologyXiangtan 411201China

The Smith form of a matrix plays an important role in the equivalence of matrix.It is known that some multivariate polynomial matrices are not equivalent to their Smith forms.In this paper,the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.

关键词： Degree-Lexicographical order equivalence of matrix multidimensional system multivariate polynomial matrix Smith form

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A Revisit to the Stability of Spatially Interconnected systems

A Revisit to the Stability of Spatially Interconnected Syste...

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第二十九届中国控制会议

作者： ZHOU Tong Department of Automation and TNList,Tsinghua University,Beijing 100084,P.R.China

A necessary and sufficient condition is derived in this paper for the stability of a linear time invariant（LTI）multidimen-sional（MD）dynamic system.This condition is expressed by a set of linear matrix inequalities（LMIs）.A special characteristic of this condition is that although the number of LMIs increases exponentially with the spatial dimension of the system,the dimensions of the LMIs are identical to each other and are of the same order as those of system matrices.Moreover,both the number and the dimensions of the LMIs are explicitly given.These properties make the derived condition particularly attractive when the spatial dimensions are low that are frequently encountered in practical applications.

关键词： Linear Matrix Inequality multidimensional system Multi-input Multi-output system Stability Spatio-Temporal system

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A New realization of multidimensional Fornasini-Marchesini Ⅱ State-space Model for MIMO Radar

A New realization of Multidimensional Fornasini-Marchesini ...

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第32届中国控制与决策会议

作者： Liu Chang Cheng Hua Zhongyong Cao Dept.of Information Science and Engineering Wuhan University of Science and Technology

In this paper,a new algorithm of solving the system realization matrix is proposed for the target detection of multi-input and multioutput radar.The algorithm is based on one-dimensional array with F-M II model to solve the implementation problem of system state space model.By setting a one-dimensional array,the array is substituted into the transfer function which is obtained by the state space model.This method is used to make the complexity of the implementation process of the system lower,and is beneficial to the analysis and design of the system.Compared with the existing image algorithms,the middle chart transformation link is omitted,the calculation step is simplified,and the realization of multi-dimensional F-M Ⅱ model is more convenient and efficient.The application of this algorithm to the MIMO radar system can improve the analysis efficiency of the system.

关键词： multidimensional system MIMO radar Fornasini-Marchesini Ⅱ model state-space realization

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QUANTIFIER ELIMINATION BASED METHOD FOR STABILIZATION OF N-DIMENSIONAL systemS

QUANTIFIER ELIMINATION BASED METHOD FOR STABILIZATION OF N-D...

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第二十届中国控制会议

作者： Jiang Qian YING Faculty of Regional Studies, Gifu University, Yanagido, Gifu 501, Japan

＜正＞Construction of stabilizing compensators （stabilizers） for general n-dimensional linear systems is an important problem in mathemitical systems theory. The construction of a stabilizing compensator for a general n-D （n ≥ 3） has been a long standing open problem. In this paper we formulate the stabilizer construction as a quantifier elimination problem, which can be solved by using the Cylindrical Algebraic Decompostion （CAD） approach. We also formulate the construction of a stable stabilizing compensator for an n-D system as a quantifier elimination problem.

关键词： multidimensional system stabililty stabilization stabilizer construction quantifier elimination.

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