BIBO stability

<p>In <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, specifically <a href="/facts/Control_theory/aIuERpn6">control theory</a>, bounded-input, bounded-output (BIBO) stability is a form of <a href="/facts/Control_theory/aIuERpn6">stability</a> for <a href="/facts/Signal_(information_theory)/41YqUJ8c">signals</a> and <a href="/facts/Control_system/8CEjIDlS">systems</a> that take inputs. If a system is BIBO stable, then the output will be <a href="/facts/Bounded_function/whVjbtuk">bounded</a> for every input to the system that is bounded.
</p><p>A signal is bounded if there is a finite value 
  
    
      
        B
        >
        0
      
    
    {\displaystyle B>0}
  
 such that the signal magnitude never exceeds 
  
    
      
        B
      
    
    {\displaystyle B}
  
, that is
</p>
For <a href="/facts/Discrete-time/RR8wpS9e">discrete-time</a> signals: 
  
    
      
        ∃
        B
        ∀
        n
        (
         
        
          |
        
        y
        [
        n
        ]
        
          |
        
        ≤
        B
        )
        
        n
        ∈
        
          Z
        
      
    
    {\displaystyle \exists B\forall n(\ |y[n]|\leq B)\quad n\in \mathbb {Z} }

For <a href="/facts/Continuous-time/RR8wpS9e">continuous-time</a> signals: 
  
    
      
        ∃
        B
        ∀
        t
        (
         
        
          |
        
        y
        (
        t
        )
        
          |
        
        ≤
        B
        )
        
        t
        ∈
        
          R
        
      
    
    {\displaystyle \exists B\forall t(\ |y(t)|\leq B)\quad t\in \mathbb {R} }

BIBO stability open-in-new

BIBO stability