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lpvweig2

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

Calling Sequence

[mus]=lpvweig2(theta)

Parameters

Theta:

Is the measured parameter varying. This could be an scalar or a vector.

mus:

It is the vector of weightings function. mus=[mu1 mu2 sum(mu)] ^T. 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 two vertices. 
This funtion is very usefull when the parameter varyin is an state of the systems (see [1]).
The function builds the weighting function  Σmu(theta) given the vertices and the measured parameters theta.

Examples

// parameter varying
theta=0.5;
mus=lpvweig2(theta)

// given a vector of measured parameters
// this it is very useful for simulation
theta=rand (1:40);
mus=lpvweig2(theta)

// plotting
figure(1);
clf();
t=1:size(mus,2);
subplot(211)  
plot(t,theta)
legend('Parameter varying')
subplot(212)
plot(t,mus)
legend('Weighting functions')

See also

Author

Bibliography

[1] Theilliol, D., & Aberkane, S. (n.d.). Design of LPV observers with unmeasurable gain scheduling variable under sensor faults. IFAC World Congress 2011.

[2] 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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