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dss2ss

Convert descriptor state-space model to explicit form

Since R2024a

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    Syntax

    sys = dss2ss(dsys)
    sys = dss2ss(dsys,"consistent")

    Description

    sys = dss2ss(dsys) eliminates the E matrix in the descriptor state-space model dsys and returns an explicit state-space model sys.

    Ex˙=Ax+Buy=Cx+Du

    dsys must be proper and sys has fewer states than dsys when E is singular (the explicit form removes the algebraic variables). Use findop to compute matching initial conditions when the state is reduced.

    example

    sys = dss2ss(dsys,"consistent") takes an array of descriptor state-space models dsys and eliminates E while preserving state consistency, that is, all models in sys share the same state vector x. This requires all E matrices to be invertible.

    Examples

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    Open Live Script

    This example shows how to use dss2ss to convert a state-space model in descriptor form to explicit form.

    For this example, consider a cube rotating about its corner with inertia tensor J and a damping force F of 0.2 magnitude. The input to the system is the driving torque while the angular velocities are the outputs. The equation is given by:

    Jdωdt+Fω=T

    y=ω

    The state-space matrices for the cube are:

    A=-F,B=I,C=I,D=0,E=J,where,J=[8-3-3-38-3-3-38]andF=[0.20000.20000.2]

    Specify the A, B, C and D matrices, and create the continuous-time descriptor state-space model.

    J = [8 -3 -3; -3 8 -3; -3 -3 8];
F = 0.2*eye(3);
A = -F;
B = eye(3);
C = eye(3);
D = 0;
E = J;
sysd = dss(A,B,C,D,E);

    To convert this model to explicit form, use dss2ss.

    syse = dss2ss(sysd);
syse.E
    ans =

     []

    As you can see, the E matrix is empty. The dss2s function provides an equivalent explicit transformation.

    sigma(sysd,syse,'r--')

    Input Arguments

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    Descriptor state-space model, specified as a state-space model or an array of state-space models.

    Output Arguments

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    Explicit state-space model, returned as a state-space model or an array of state-space models.

    Version History

    Introduced in R2024a

    See Also

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