L∞ Set-membership Estimation for Continuous-time Switched Linear Systems

In this work, we focuses on the problem of designing an interval state estimation for continuous-time Switched Linear Systems (SLS) in the Unknown But Bounded Error (UBBE) context. To do so, we design a new structure of interval observers by introducing weighted matrices not only to give more degrees of design freedom but also to attenuate the conservatism caused by uncertainties. Observer gains are derived from the solution of Linear Matrix Inequalities (LMIs), based on the use of a common Lyapunov function, to ensure cooperativity and stability. An L
∞
technique is then introduced to compensate the measurement noise and disturbances’ effects and to enhance the precision of interval estimation. Finally, numerical simulations are given, evaluating the proposed methodology and demonstrating its effectiveness.