T-N-L Interval Observer Design for Linear Continuous Time Invariant Systems with $L_{\infty}$ Performance

This paper addresses the design problem of interval observers for Linear Continuous-Time Invariant Systems (LCTIS) in the set-membership framework. To achieve this, weighted matrices have been introduced to obtain a new structure for interval observers. This provides greater design flexibility and reduces the conservatism due to uncertainties. By solving Linear Matrix Inequalities (LMIs), observer gains are determined based on the use of a candidate Lyapunov function, ensuring both stability and cooperativity. In order to improve the interval estimation accuracy, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> approach is then applied, compensating the measurement noise and disturbances' effects. Finally, numerical simulations evaluate the proposed technique, demonstrating its effectiveness.