Multi-Objective H∞/ <i>r</i> -Stability Optimal Interval Estimation for Linear Discrete-Time Systems and Application to DC Servo Motor

The main goal of this brief is to present a methodology to design multi-objective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{H}_{\infty } $ </tex-math></inline-formula>/r -stability interval estimation for linear discrete-time systems affected by bounded, but unknown disturbances. Compared with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{H}_{\infty } $ </tex-math></inline-formula> norm criterion that is used to reject the influence of external disturbances on the output under the worst scenario, multi-objective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm{H}_{\infty } $ </tex-math></inline-formula>/r-stability interval observer takes pole-placement into account, the poles of the system matrix of the observes are configured as close as possible to the origin. This is to ensure not only a relatively fast convergence characteristic but also the minimum interval width. Finally, an illustrative example of a DC servo motor highlights the performance of our methodology.