Observer Design for Space-Varying Delayed Distributed Parameter Systems

This paper considers the observer design problem of the space-varying delayed distributed parameter systems (DPSs) described by parabolic partial differential equations (PDEs). By using a Lyapunov-Krasovskii functional, an observer design is developed by spatial linear matrix inequalities (SLMIs) to ensure the exponential stability for the estimation error delayed DPS. In addition, to solve the SLMIs, the observer design for space-varying delayed DPS is formulated as an LMI feasibility problem. Finally, we verify the effectiveness of the proposed method via an example.