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I have a 2nd order of sliding mode observer of the form:

[tex] \dot{\hat{x}} = \hat{f}(x,t) + \delta f + \Psi(u,y) +[ \frac{d \Omega}{dx}]^{-1} \upsilon[/tex]

where ##\upsilon##:

[tex] \upsilon_1= \alpha_1 \lambda_1^{1/2} | y_1 -\hat{x}_1|^{1/2}*sign(y_1 -\hat{x}_1)[/tex]

[tex]\upsilon_2= \alpha_2 \lambda_1*sign(\upsilon_1)[/tex]

[tex] \upsilon_3= \alpha_3 \lambda_2^{1/2} | y_2 -\hat{x}_2|^{1/2}*sign(y_2 -\hat{x}_2)[/tex]

[tex]\upsilon_4= \alpha_4 \lambda_2*sign(\upsilon_3)[/tex]

....

where ##y_{1,2}## is the output and and ##x_{1,2}## are the estimations of measurable outputs. How do I find the correct gain of sliding mode observer?

##\delta f## is the uncertainties and ##[ \frac{d \Omega}{dx}]^{-1} ## is some mathematical stuff based on transformations. The main question is how do you find the proper gain of an observer by linearizing a system?

Do I linearize the plant and observer? and then what graphs should I look at to find the appripriate gains?

Thanks in advance