mat2dec

Extract vector of decision variables from matrix variable values

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Syntax

decvars = mat2dec(lmisys,X1,...,Xk)

Description

decvars = mat2dec(lmisys,X1,...,Xk) computes the vector of decision variables corresponding to the values X1,...,Xk of the matrix variables in the LMI system lmisys. The decision variables are the independent entries of the matrices X1, . . ., Xk and constitute the free scalar variables in the LMI problem. This function is useful, for example, to initialize the LMI solvers mincx or gevp. Given an initial guess for X1, . . ., XK, mat2dec forms the corresponding vector of decision variables xinit.

example

Examples

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Suppose that you have already defined an LMI system lmisys with two matrix variables X and Y, where

  • X is a symmetric block diagonal with one 2-by-2 full block and one 2-by-2 scalar block.

  • Y is a 2-by-3 rectangular matrix.

Compute the decision-variable values corresponding to the following particular instances of X and Y.

X0 = [1  3 0 0; 
      3 -1 0 0;
      0  0 5 0;
      0  0 0 5];
Y0 = [1 2 3;
      4 5 6];

Use mat2dec to get the vector of decision-variable values.

decvars = mat2dec(lmisys,X0,Y0);
decv'
ans = 
        1     3     -1     5     1     2     3     4     5     6

decv is of length 10, because Y has six free entries while X has only four independent entries due to its structure. Use decinfo to obtain more information about the decision variable distribution in X and Y.

Input Arguments

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LMI system, specified as a vector. After defining the LMI system in MATLAB® as described in Specify LMI System at the Command Line, use getlmis to get this vector representation of the system.

Values for the matrix variables of the LMI represented by lmisys. The dimensions and structure of X1,...,Xk must be consistent with the description of X1, . . ., XK in lmisys.

Output Arguments

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Decision-variable values corresponding to matrix-variable values X1,...,Xk, returned as a vector.

Version History

Introduced before R2006a

See Also

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