Output Feedback Control of Coupled Linear Parabolic ODE–PDE–ODE Systems

This article deals with the backstepping design of observer-based compensators for parabolic ODE–PDE–ODE systems. The latter consist $\boldsymbol {n}$ coupled PDEs distinct diffusion coefficients and spatially-varying coefficients, that are bidirectionally to ODEs at both boundaries. actuation sensing appears through these resulting in a challenging control problem. For this setup systematic approach is proposed, order determine state feedback controller an observer. In particular, loop observer error dynamics mapped into stable cascades by making use sequence transformations. With this, can be traced back solution kernel equations already found literature as well initial boundary value problems, solved numerically. Exponential stability closed-loop system verified, wherein decay rate directly specified design. results illustrated output unstable two PDEs.