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When searching for values of the model parameters that best fit the measured ste...

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When searching for values of the model parameters that best fit the measured step response of the

system, we did not add any constraints on the parameters. If we only wanted to search over stable

models, what constraint must the parameters a

₁ and a₂ satisfy?

a₁>0 and a₂<0

No additional conditions, the models will be stable for any choice of a₁ and a₂.

|a₁|<1 and |a₂|<1

Re(a₁)<0 and Re(a₂)<0

It is not enough to constrain a₁ and a₂

only to ensure stability of the resulting models. We

also need to add constraints on the other parameters (such as K

₁ and K₂, or τ or T_room).

a₁<0 and a₂<0

a₁>0 and a₂>0

a₁<0 and a₂>0

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