Several Problems Of Feedback Control System And Matrix Approx Imation

The contents of this thesis are divided into two parts: the first part isconcerned with the problems of the feedback control system, whichare included in Chapter2,Charter3and Chapter4; the second one isdevoted to matrixapproximation problem researches, includingChapter5and Chapter6. Specific as follows:1. Basic properties of the right invertible systemBy applying the canonical decomposition of the right invertiblesystem, we deduce equivalent conditions of controllability, stability bystate feedback and observability of a right invertible system fC; A;Bg.We also derive three equivalent sufficient conditions of the non-regularrow-by-row decoupling problem.2. All solutions and pole assignments of the regular systemdecoupling problemsBy applying the canonical decomposition of the right invertiblesystem, we study the row-by-row decoupling problem and thetriangular decoupling problem for regular system. We deduce allsolutions of the row-by-row decoupling problem and triangulardecoupling problem. At the same time, by applying the explicitexpression of the feedback matrix, we further discuss the poleassignment problem. For any given poles, we obtain the explicitexpression of the transfer matrix.Finally, we give numerical examples to illustrate our results.3.The minimum rank solutions to the matrix approximation problemin spectral normWe deduce the minimum rank solutions, minimum rank (skew)Hermitian solutions to the matrix approximation problem in spectralnorm by applying the norm-preserving dilation theorem, the R-SVD, theH-SVD and the S-H-SVD, respectively. All explicit expressions of the minimum rank solutions are obtained.