Uncontrollable States in State Space

A repeated row in the controllability matrix implies that there are redundant inputs in the system.In summary, the controllability matrix indicates the existence of an uncontrollable part of a linear state space system, but does not specify which state is uncontrollable. A repeated row in the matrix suggests the presence of redundant inputs in the system.
  • #1
Eidos
108
1
Hi Guys/Gals

If you end up with a row of zeros in the controllability matrix for a linear state space system, does that row correspond with the state that is uncontrollable


eg. Assuming a linear state space system with 5 states, a row of zeros in the 4th row of the controllability matrix corresponds to the 4th state of the system being uncontrollable.

Secondly, if we have a repeated row in the controllability matrix what does that imply?

Thanks :smile:
 
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  • #2
The controllability matrix does not tell you which state is uncontrollable. A row of zeros or in general, controllability matrix which does not have full rank indicates the existence of an uncontrollable part of your system.

You can transform your system with a Kalman controllable/uncontrollable decomposition and see which states are uncontrollable.
 

Related to Uncontrollable States in State Space

1. What are uncontrollable states in state space?

Uncontrollable states in state space refer to the states of a system that cannot be directly controlled or manipulated by the system's inputs or control variables. These states can only be influenced indirectly through the system's dynamics and the values of its controllable states.

2. How do uncontrollable states affect a system?

Uncontrollable states can significantly impact the behavior and performance of a system. They can introduce unexpected or undesirable dynamics, make it difficult to achieve desired outcomes, and limit the system's controllability.

3. How do scientists deal with uncontrollable states in state space?

Scientists use various techniques to handle uncontrollable states in state space, such as system identification, model reduction, and controller design. These methods aim to identify and eliminate or mitigate the effects of uncontrollable states on the system's behavior.

4. Are uncontrollable states always undesirable?

Not necessarily. In some cases, uncontrollable states can have a stabilizing effect on a system, making it more resilient to disturbances. However, they can also make it challenging to achieve specific control objectives, so they are generally considered undesirable.

5. Can uncontrollable states be eliminated entirely?

No, uncontrollable states are inherent to a system's dynamics and cannot be entirely eliminated. However, scientists can use various techniques to reduce their impact on the system's behavior and improve its controllability.

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