Interval observer for Linear Time Invariant (LTI) uncertain systems with state and unknown input estimations

In this paper, the problem of interval observer design for LTI uncertain systems is addressed. The aim is to estimate simultaneously the upper and lower bounds of unmeasurable states and unknown inputs. Based on a set membership approach, the proposed method interest consists in reducing the estimate conservatism assuming that all known and unknown inputs, disturbances, uncertainties and noises are bounded with a priori known bounds. For that, decoupling methods are used to reduce the latter propagation. The estimation problem is led back to a singular model representation. An example is given to illustrate the proposed design method.