On Reduced-Order Linear Functional Interval Observers for Nonlinear Uncertain Time-Delay Systems with External Unknown Disturbances

Interval functional observers for time‐delay systems with additive disturbances

“…Conversely, we will prove that if the LP problem (49) is feasible then conditions (12) to (14) and (42) are satisfied. Indeed, the observer gains T i , J i (i = 0,1,2, … ,q) are now obtained as in (44) to (46), where Z = (diag( )) −1  T .…”

“…Proposition 1. Conditions (12 ) to (14 ) and (42 ) are feasible if and only if the following LP problem with the variables ∈ R r and  ∈ R (q+1)(r+p)×r is feasible:…”

“…Proof. First, we assume that (12) to (14) and (42) are feasible. If (42) holds, then the general solution of (38) is given in (43).…”

“…This follows that a solution for (38) exists, that is, condition (42) holds. Moreover, by using Z = (diag( )) −1  T , from the four inequalities in the LP problem (49), we can easily see that conditions (12) to (14) are satisfied. The proof is complete.…”

“…Our interval observers utilize multiple delayed output measurement and they have a more general structure than those currently available in the literature. By having such a new structure, we can overcome some drawbacks of previous work, 11,12 and we can design interval functional observers for a wider class of time-delay systems with additive disturbances than those reported in References 11 and 12. Comparison and discussions will be given to show the effectiveness of our proposed interval functional observers and design method.…”