bloc2ss block-diagram to state-space conversion

## Syntax

    sl = bloc2ss(blocd)

## Arguments

blocd

  list

sl

  list

## Description

Given a block-diagram representation of a linear system `bloc2ss` converts this representation to a state-space linear system. The first element of the list `blocd` must be the string `'blocd'`. Each other element of this list is itself a list of one the following types :

    list('transfer','name_of_linear_system')

    list('link','name_of_link',
                 [number_of_upstream_box,upstream_box_port],
                 [downstream_box_1,downstream_box_1_portnumber],
                 [downstream_box_2,downstream_box_2_portnumber],
                 ...)

The strings `'transfer'` and `'link'` are keywords which indicate the type of element in the block diagram.

Case 1 : the second parameter of the list is a character string which may refer (for a possible further evaluation) to the Scilab name of a linear system given in state-space representation (`syslin` list) or in transfer form (matrix of rationals).

To each transfer block is associated an integer. To each input and output of a transfer block is also associated its number, an integer (see examples)

Case 2 : the second kind of element in a block-diagram representation is a link. A link links one output of a block represented by the pair `[number_of_upstream_box,upstream_box_port]`, to different inputs of other blocks. Each such input is represented by the pair `[downstream_box_i,downstream_box_i_portnumber]`.

The different elements of a block-diagram can be defined in an arbitrary order.

For example

[1] `S1*S2` with unit feedback.

There are 3 transfers `S1` (number `n_s1=2`) , `S2` (number `n_s2=3`) and an adder (number `n_add=4`) with symbolic transfer function `['1','1']`.

There are 4 links:

- The first one (named `'U'`) links the input (port 0 of fictitious block -1, omitted) to port 1 of the adder.
- The second one links the (output)port 1 of the adder to the (input)port 1 of system `S1`.
- The third one links the (output)port 1 of `S1` to the (input)port 1 of `S2`.
- The fourth link (named `'Y'`) links (output)port 1 of `S2` to the output (port 0 of fictitious block -1, omitted) and to (input)port 2 of the adder.

## Examples

    //Initialization
    syst=list('blocd'); l=1;

    //Systems
    l=l+1;
    n_s1=l;
    syst(l)=list('transfer','S1');  //System 1
    l=l+1;
    n_s2=l;
    syst(l)=list('transfer','S2');  //System 2
    l=l+1;
    n_adder=l;
    syst(l)=list('transfer',['1','1']);  //adder

    //Links
    // Inputs  -1 --> input 1
    l=l+1;
    syst(l)=list('link','U1',[-1],[n_adder,1]);

    // Internal
    l=l+1;
    syst(l)=list('link',' ',[n_adder,1],[n_s1,1]);
    l=l+1;
    syst(l)=list('link',' ',[n_s1,1],[n_s2,1]);

    // Outputs // -1 -> output 1
    l=l+1;
    syst(l)=list('link','Y',[n_s2,1],[-1],[n_adder,2]);

With `s=poly(0,'s'); S1=1/(s+1);S2=1/s;` the result of the evaluation call `sl=bloc2ss(syst);` is a state-space representation for `1/(s^2+s-1)`.

[2] Example of LFT (Linear Fractional Transformation):

    //Initialization
    syst=list('blocd');
    l=1;

    //System (2x2 blocks plant)
    l=l+1;
    n_s=l;
    syst(l)=list('transfer',['P11','P12';'P21','P22']);

    //Controller
    l=l+1;
    n_k=l;
    syst(l)=list('transfer','k');

    //Links
    l=l+1;
    syst(l)=list('link','w',[-1],[n_s,1]);
    l=l+1;
    syst(l)=list('link','z',[n_s,1],[-1]);
    l=l+1;
    syst(l)=list('link','u',[n_k,1],[n_s,2]);
    l=l+1;
    syst(l)=list('link','y',[n_s,2],[n_k,1]);

With

    A=[0,1;0,0];
    B=[1;1];
    C=[1,1];
    D=poly(0,'s');
    P=syslin('c',A,B,C,D);

## See also

- poly