On the Morgan problem with stability

where the polynomial matrices Ni(s) and D(s) form a normal external description (NED) of (C, A H ) ; see [11]. The matrices N(s) := CNx(s) and D(s) then form, not necessarily coprime, a matrix fraction description (MFD) of (C,A,B). Recall that Ni(s) and D(s) are right coprime with D(s) being column reduced. The column degrees, Cj := degciD(s), i = 1,2,... ,m, are the controllability indices of (C, A, B). We shall further assume (see [8] for more details) that V* = TV, where TV denotes the maximal controllability subspace lying in Ker C and V* is the maximal (A,B)invariant subspace contained in Ker C.

[1]  A. Morse,et al.  Status of noninteracting control , 1971 .

[2]  VLADIMÍR KUČERA,et al.  Constant solutions of polynomial equations , 1991 .

[3]  Vladmír Kučera.  Static realization of dynamic precompensators for descriptor , 1991 .

[4]  P. Falb,et al.  Decoupling in the design and synthesis of multivariable control systems , 1967, IEEE Transactions on Automatic Control.

[5]  Yu. A. Gur'yan,et al.  Parts I and II , 1982 .

[6]  Static realization of dynamic precompensators , 1992 .

[7]  Michel Malabre,et al.  The row by row decoupling problem with stability: a structural approach , 1994, IEEE Trans. Autom. Control..

[8]  L. Pernebo.  An Algebraic Theory for the Design of Controllers for Linear Multirate Systems Part I: Structure Matrices and Feedforward Design , 1981 .

[9]  V. Eldem.  The solution of diagonal decoupling problem by dynamic output feedback and constant precompensator: the general case , 1994, IEEE Trans. Autom. Control..

[10]  J. Descusse,et al.  Solution to Morgan's problem , 1988 .

[11]  O. Sename,et al.  Decoupling of linear systems with delays , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  V. Eldem,et al.  Diagonal Decoupling Problem with Internal Stability: A Solution by Dynamic Output Feedback and Constant Precompensator , 1995 .

[13]  J. Dion,et al.  The minimal delay decoupling problem: feedback implementation with stability , 1988 .

[14]  Jr. B. Morgan.  The synthesis of linear multivariable systems by state-variable feedback , 1964 .

[15]  Jean-François Lafay,et al.  The row-by-row decoupling via state feedback: A polynomial approach , 1993, Autom..

[16]  Vasfi Eldem.  Feedback realization of open loop diagonalizers , 1993, Kybernetika.

[17]  L. Pernebo.  An algebraic theory for design of controllers for linear multivariable systems--Part II: Feedback realizations and feedback design , 1981 .

[18]  V. Kučera,et al.  Reachability and controllability indices for linear descriptor systems , 1990 .