Skip to main content
MathOverflow

Return to Question

Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Bumped by Community user
Minor edits
Source Link
edit approved Jan 2, 2018 at 7:11
Rodrigo de Azevedo
edit approved Jan 2, 2018 at 7:11
Rodrigo de Azevedo
  • 1
  • 3
  • 16
  • 35

In general, when we talk about controllability, we talk about proving the existence of a control to remaininput that transfers the state to anothera desired state at a desired time $T$. However, but inwhen we talk about stability, we prove that the solution tends to zero when $T$time tends to infinity.

My question is: Is there any relation between the stability (exponential, polynomial, strong) and the controllability (approximate or exact, null) of PDEPDEs?

In general when we talk about controllability we talk about proving the existence of control to remain the state to another state at desired time $T$, but in stability we prove that the solution tends to zero when $T$ tends to infinity.

My question is: Is there any relation between stability (exponential, polynomial, strong) and controllability (approximate or exact, null) of PDE?

In general, when we talk about controllability, we talk about proving the existence of a control input that transfers the state to a desired state at a desired time $T$. However, when we talk about stability, we prove that the solution tends to zero when time tends to infinity.

Is there any relation between the stability (exponential, polynomial, strong) and the controllability (approximate or exact, null) of PDEs?

Bumped by Community user
Bumped by Community user
Bumped by Community user
Corrected some English typos. Sitill unclear: "remain the state".
Source Link
edit approved Oct 3, 2017 at 1:58
jeq
edit approved Oct 3, 2017 at 1:58
jeq
  • 1.2k
  • 5
  • 16
  • 21

Relation between controlabilitycontrollability and stability of PDE

In general when we talk about controlabilitycontrollability we talk about proving the existence of control to remain the state to another state at desired time $T$, but in stabilitystability we proofprove that the solution tends to zero when tt$T$ tends to infinity, my.

My question is: Is there any relation between stability  (exponential, polynomial, strong) and controlabilitycontrollability (approximate or exact, null) of PDE? Thank you.

Relation between controlability and stability of PDE

In general when we talk about controlability we talk about proving the existence of control to remain the state to another state at desired time $T$, but in stability we proof that the solution tends to zero when tt tends to infinity, my question is: Is there any relation between stability(exponential, polynomial, strong) and controlability(approximate or exact, null) of PDE? Thank you.

Relation between controllability and stability of PDE

In general when we talk about controllability we talk about proving the existence of control to remain the state to another state at desired time $T$, but in stability we prove that the solution tends to zero when $T$ tends to infinity.

My question is: Is there any relation between stability  (exponential, polynomial, strong) and controllability (approximate or exact, null) of PDE?

Source Link
Gustave
Gustave
  • 617
  • 3
  • 8

Relation between controlability and stability of PDE

In general when we talk about controlability we talk about proving the existence of control to remain the state to another state at desired time $T$, but in stability we proof that the solution tends to zero when tt tends to infinity, my question is: Is there any relation between stability(exponential, polynomial, strong) and controlability(approximate or exact, null) of PDE? Thank you.