The author solves the problem of reducing several complex (generally speaking) nxn matrices to the same block-triangular form with a maximum possible number of blocks on the main diagonal with the use of a similarity ...
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The author solves the problem of reducing several complex (generally speaking) nxn matrices to the same block-triangular form with a maximum possible number of blocks on the main diagonal with the use of a similarity transformation. The obtained solution may be used to apply the methods of hierarchical decomposition in the analysis of complex systems.
Adaptive control of a class of uncertain multi-input/multi-output (MIMO) non-linear systems in block-triangular forms is considered in this paper. By incorporating dynamic surface approach and "minimal learning p...
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Adaptive control of a class of uncertain multi-input/multi-output (MIMO) non-linear systems in block-triangular forms is considered in this paper. By incorporating dynamic surface approach and "minimal learning parameters" algorithm, a systematic procedure for the synthesis of stable adaptive fuzzy tracking controllers with less tuning parameters is developed. Takagi-Sugeno (T-S) fuzzy logic systems (FLSs) are used to approximate those unstructured system functions rather than the unknown virtual control gain functions. Consequently, the potential controller singularity problem can be overcome. Moreover, both problems of "explosion of learning parameters" and "explosion of complexity" are avoided. The computational burden has thus been greatly reduced. The stability in the sense of semi-globally uniform ultimate boundedness (SGUUB) of the closed-loop MIMO systems is established via Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the effectiveness and the advantages of the proposed control approach.
In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsyste...
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In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.
An algorithm for separating a rational matrix relative to the imaginary axis (the unit circle), that is, for representing it by the sum of two matrices each of which has poles only in the left- or right-hand half-plan...
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An algorithm for separating a rational matrix relative to the imaginary axis (the unit circle), that is, for representing it by the sum of two matrices each of which has poles only in the left- or right-hand half-plane (inside or outside the unit circle), is presented. The feasibility Of iterative refinement of the obtained result is demonstrated. The refinement procedure is reduced to the construction of a solution of a system of Sylvester equations. It is shown that the algorithm can be used without a preliminary construction of a minimal realization of the original matrix.
In this paper, we set up a geometric framework for solving sparse rnatrix problems. We introduce geometric sparseness, a notion which applies to several well-known families of sparse matrix. Two algorithms are present...
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In this paper, we set up a geometric framework for solving sparse rnatrix problems. We introduce geometric sparseness, a notion which applies to several well-known families of sparse matrix. Two algorithms are presented for solving geometrically-sparse rnatrix problems. These algorithms are inspired by techniques in classical algebraic topology, and involve the construction of a simplicial complex from certain data on the matrix. In both cases, large parts of the computation can be parallelised. (C) 2003 Elsevier Inc. All rights reserved.
A partitioned matrix, of which the column- and row-sets are divided into certain numbers of groups, arises from a mathematical formulation of discrete physical or engineering systems. This paper addresses the problem ...
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A partitioned matrix, of which the column- and row-sets are divided into certain numbers of groups, arises from a mathematical formulation of discrete physical or engineering systems. This paper addresses the problem of the block-triangularization of a partitioned matrix under similarity/equivalence transformation with respect to its partitions of the column- and row-sets. Such block-triangularization affords a mathematical representation of the hierarchical decomposition of a physical system into subsystems if the transformation used is of physical significance. A module is defined from a partitioned matrix, and the simplicity of the module is proved to be equivalent to the nonexistence of a nontrivial block-triangular decomposition. Moreover, the existence and the uniqueness of the block-triangular forms are deduced from the Jordan-Holder theorem for modules. The results cover many block-triangularization methods hitherto discussed in the literature such as the Jordan normal form and the strongly connected-component decomposition in the case of partition-respecting similarity transformations, and the rank normal form, the Dulmage-Mendelsohn decomposition, and the combinatorial canonical form of layered mixed matrices in the case of partition-respecting equivalence transformations.
A computer program for obtaining a permutation of a general sparse matrix that places a maxunum number of nonzero elements on its dmgonal is described. The history of this problem and the mare motivatmn for developing...
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