Hello,(adsbygoogle = window.adsbygoogle || []).push({});

In a linear system of the form $$\dot{x}=Ax+Bu$$ and $$y=Cx$$ we can use state feedback control $$u=Kx$$ assuming we know the state, or can observe it, to control the system if (A,B) is controllable (all states are reachable).

How does the theory on controllability apply to output feedback? So that the feedback is not taken from the state of the system using an observer, but from the output.

If the original system (A,B) is not controllable, is it also true that no OUTPUT feedback law exists to control the system from any initial condition?

My initial reaction is that the system is controllable from neither the state feedback or output feedback methods. My basis for this assumption is that the theory of controllability is fundamentally based on the system (A,B), and is not developed from the starting point of any feedback. But I am unsure.

Sorry if my question is not well posed - any information appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear control system controllability

**Physics Forums | Science Articles, Homework Help, Discussion**