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DeCaToKi >> en_US > c2dd

c2dd

This function convert a Continuos Descriptor system into a Discrete Descriptor system in restricted system Equivalence form

Calling Sequence

[E1t,Ad, B1t,B2t]=c2dd (E,A,B,Te)

Parameters

E, A, B:

Continuos matrices of descriptor system. E singular

E1t, Ad, B1t, B2t:

Discrete equivalent matrices

Te:

Sample Time

Description

Given a Descriptor system in the form
dxEdt=Ax+Bu
y   =Cx+Du
The equivalent discrete descriptor system is (See Karampetakis, (2003) and *.pdf in /.../DeCaToKi/doc path)  
x1((k+1)T)   = Adx1(kT)+B1tu(kT)
E1tx2((k+1)T)= x2(kT)+B2tu(kT)
E1t is a Nilpotent Matrix and the equivalent discrete system is in r.s.e standar form.

Examples

// Descriptor system

E=[1 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0] ;
A=[-0.8775 0 0.526 -0.0274;
  -5.8500  -0.5 0.1481 0.0026; 
  0      0.5   -1     0.2;
  0      2.6522  -0.274  -2];
B=[ 0 0; -0.0856  0.01; 0 0; 0 1];
C=[1 1 0 1; 0 0 1 1;0 0 1 0];
// Convert to descriptor form
Te=0.1; //seg
[E1t,Ad, B1t,B2t]=c2dd (E,A,B,Te)

See also

Author

Bibliography

[1] Karampetakis, N. P, (2003). On the discretization of singular systems. IMA Journal of Mathematical Control and Information. Vol. 21, pp. 223-242

[2] Koumboulis, F. N. and Mertzios,(1999), B. G. on Kalman Controlability and Observability Criteria for Singular Systems Circuits Systems and Signals, 18, 269-290

[1] Lewis, F. L. (1985). Fundamental, reachability, and observability matrices for discrete descriptor systems. IEE Transactions on Automatic Control 30(5), 502–505.

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