Hello, I am wondering about the essential question of Simultaneous stabalization. I know it is different from robust stabalization (which stabalizes an infinite number of plants) in that the controller must stabalize a finite number of plants that are not interrelated.
My basic questions :1) Do the plants being stabalized HAVE to include non-stable plants? Is it meaningful to prove a controller exists which stabalizes a finite number of stable plants?
2) Strong stabalization means the controller has to be stable too. Is this a necessary condition for the Simultaneous stabalization solution? I mean if one can find a controller which stabalizes a finite number of plants, does the controller HAVE to be stable? Or is it ok to just find any controller which stabalizes the plants?
I would appreciate any advice, references, etc... Thanks. Best regards, Jon