Assessment and Future Directions of Nonlinear Model Predictive ...

62 M.V. Kothare and Z. Wanmodel e(k +1) = (A(k) − L p C(k)) e(k) with [ A(k) T C(k) T ] T∈ Ψ. For all[ ( )] T Tx, ˆx ∈ Π x and u ∈ Π u , the Jacobian matrix ∂f ( ∂h) T∈ Ψ with∂x ∂x⎡ ∂f 1⎡∂x 1··· ∂f1∂h 1∂x n∂x 1··· ∂h1∂x n∂f∂x= ⎢ . ⎣ . .. ⎥ ∂h. ⎦ and∂x= ⎢ . .⎣ . ... .⎥⎦ . It is straight forward to⎤∂f n∂x 1··· ∂fn∂x n⎤∂h q∂x 1··· ∂hq∂x nestablish the exponential convergence of the observer and the norm bound ofthe state estimation error within S based on the LTV model and the nonlinearmodel.