smybolicEquations

Outputs the mss-model as symbolic equations

Contents

Syntax

symbolicEquations(msys)
[xp,y]=symbolicEquations(msys)

Description

symbolicEquations(msys) Outputs the state equations of the multilinear state-space object msys as a symbolic equation.

[xp,y]=symbolicEquations(msys) Outputs the state equations xp and the output equations y of the multilinear state-space object msys as a symbolic equation.

Note that this command requires the Symbolic Math Toolbox from Matlab.

Input Arguments

msys multilinear state-space model of type mss in CPN1 format

Output Arguments

xp vector or scalar of the state equations as symbolic equations

y vector or scalar of the output equations as symbolic equations

Example 1

Firstly we can create a random continuous-time system with n=2 states, m=1 input, p=2 output, and
a rank of r=4:
   msys=rmss(2,1,2,4)
msys = 

  mss with properties:

        F: [1×1 CPN1]
        G: [1×1 CPN1]
        n: 2
        m: 1
        p: 2
    ntype: '1'
       ts: 0

Then we can check the equations by:

   [xp,y]=symbolicEquations(msys)
 
xp =
 
(10019847143879479617130564704405*u1)/81129638414606681695789005144064 + (5446107898113957435312448814475*x2)/40564819207303340847894502572032 + 25080151865133454224759707479125/81129638414606681695789005144064
 (2364521389257206159142764184533*u1)/40564819207303340847894502572032 + (4597976788001104214284280469943*x1)/10141204801825835211973625643008 + 24510632067871052468972673242447/40564819207303340847894502572032
 
 
y =
 
                                                                                                         405915346306581/1125899906842624
(8596451650578180963667417106255*x1)/40564819207303340847894502572032 + 24715625766144926850242585950385/40564819207303340847894502572032
 

Example 2

Assume we have the following second-order explicit MTI model with 2 states and 1 input $\dot{\mathbf{x}}=\left(\begin{array}{cc} x_2 + x_1x_2\\ 3u_1 + 2x_2 - 3u_1x_1 + 2x_1x_2 \end{array}\right)$. We write the explicit MTI model as a CPN1 object by defining the structural matrix S to form the monomial

    S=[0.5 -0.5; 1 0; 0 1];

and the parameter matrix with corresponding coefficients of the summands:

    phi=[2 0; 4 6];

Then we can create explicit MTI model as a CPN1 object and the mss-object:

    obj=CPN1(S,phi);
    msys=mss(obj);

To display the equations, simply use:

    [xp]=symbolicEquations(msys)
 
xp =
 
                    2*x2*(x1/2 + 1/2)
4*x2*(x1/2 + 1/2) - 6*u1*(x1/2 - 1/2)
 

To get the expanded form, we can use the expand() command of the Symbolic Math Toolbox.

    expand(xp)
 
ans =
 
                     x2 + x1*x2
3*u1 + 2*x2 - 3*u1*x1 + 2*x1*x2
 

See also

mss, rmss