Simultaneous state and process fault estimation in linear parameter varying systems using robust quadratic parameter varying observers

This article undertakes the problem of simultaneous estimation of state and process faults in linear parameter varying systems. For this purpose, a novel strategy that exploits recent results on the design of observers for quadratic parameter varying systems is developed, and a complete design procedure is described. First, it is shown that by treating the process faults as additional states to be estimated, the arising augmented state-space model is indeed expressed as a quadratic parameter varying system. Hence, the estimates provided by a quadratic parameter varying observer based on the so-called linear output error injection principle would comprise both the actual state and the process faults estimates. Robust design conditions that minimize the effect of disturbances and measurement noise on some linear, and possibly parameter-varying, combination of error variables are obtained using a Lyapunov-based approach. Then, it is shown that the design problem can be reduced to a finite set of linear matrix inequalities that can be solved using available computational tools. The final part of the article exhibits an illustrative example, which clearly exposes the potential applicability and performance of the developed approach.