Rune Allnor wrote:

> bhupala@gmail.com wrote:
> 
>>Hello all,
>>
>>How to put the constraint that the IIR filter which I design, is always
>>stable using matrix notation?
> 
> 
> Disclaimer: Guesswork to follow.
> 
> You would have to formulate the IIR filter in matrix notation,
> I suspect you end up with a state space model. If so, I
> would not be at all surprised if it turns out that the eigenvalues
> of the state transition matrix have to be positive with
> magnitudes < 1, or something like that.
> 
> Usually, eigenvalues tell as much about ssyetm stability
> in matrix notation, as pole locations tell in "standard"
> notation.
> 
> Rune
> 
You would end up with a state space model, and the resulting system 
would be stable if the eigenvalues of the state transition matrix had 
absolute values < 1 (there's no need for them to be positive, although 
negative values would cause odd ringing effects).

-- 

Tim Wescott
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bhupala@gmail.com wrote:
> Hello all,
>
> How to put the constraint that the IIR filter which I design, is always
> stable using matrix notation?

That depends on the method. How are you designing the IIR filter? For
example, if you are using time domain techniques like Prony's or
Shank's, you need to find a stable allpole filter. This can be achieved
with a slight modificiation of the algorithms.

Regards,
Andor

bhupala@gmail.com wrote:
> Hello all,
>
> How to put the constraint that the IIR filter which I design, is always
> stable using matrix notation?

Disclaimer: Guesswork to follow.

You would have to formulate the IIR filter in matrix notation,
I suspect you end up with a state space model. If so, I
would not be at all surprised if it turns out that the eigenvalues
of the state transition matrix have to be positive with
magnitudes < 1, or something like that.

Usually, eigenvalues tell as much about ssyetm stability
in matrix notation, as pole locations tell in "standard"
notation.

Rune

Hello all,

How to put the constraint that the IIR filter which I design, is always
stable using matrix notation?

thank you

sri hari