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lpvweig4

This function generates wieighting function for a Polytopic Linear Parameter Varying Descriptor System of four vertices

Calling Sequence

[mus]=lpvweig4(Theta,vert)

Parameters

Theta:

Is the vector of measured parameter. This could be an scalar or a vector. E.g. Theta=[Theta1 Theta2]= [0.04 0.1]

vert:

Are the maximun and minimun limits of the parameters. E.g. vert=[minTheta1 maxTheta1; minTheta2 maxTheta2]=[-0.05 0.05; -0.1 0.1]. Usuallly it is constant.

mus:

It is the vector of weightings function. mus=[mu1 mu2 mu3 mu4 sum(mu)]. sum(mu) =1 for all time

Description

Given a polytopic LPV Descriptor system in the form
M
dxEdt= Σmu(theta)[A(theta) x(t) + B(theta) u(t) +R(theta) d (t)]
i=1
y   =C x(t) + D u(t) 

Where theta is the parameter varying and it is bounde by four vertices.
The function builds the weighting function  Σmu(theta) given the vertices and the measured parameters theta.

Examples

// parameter varying
theta1=[-0.05 0.05]; //[ ]
theta2=[-0.1 0.1 ];
vert=[theta1; theta2] // vertices of the polytope

// for one vector
Thetas=[0.04  -0.1]
[musa]=lpvweig4(Thetas,vert)

// given a vector of measured parameters
// this it is very useful for simulation
Theta1=prbs_a(length(0:101),10)/20;
Theta2=prbs_a(length(0:101),10)/10;
Thetas=[Theta1; Theta2];
[musa]=lpvweig4(Thetas,vert)
// for a column vector 
Theta1=Theta1';
Theta2=Theta2';
Thetas=[Theta1 Theta2];
[musa]=lpvweig4(Thetas,vert)

// plotting
figure(1);
clf();
t=1:size(musa,1);
subplot(211)  
plot(t,Thetas)
legend('Parameter varying')
subplot(212)
plot(t,musa)
legend('Weighting functions')

See also

Author

Bibliography

[1] M., Hamdi., Rodrigues, M., Mechmeche, C., Theilliol, D., Braiek, N. B., & Tunisie, E. P. D. (2009). State Estimation for Polytopic LPV Descriptor Systems : Application to Fault Diagnosis. Convergence (pp. 438-443).

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