A Necessary Conditions for Optimal Steady State

We present the necessary conditions for the steady state minimum in the problem described by Equations (8.4)-(8.7) on p. 248. 

Let u be the optimal control under steady state with the corresponding state y, and multipliers A, p, and i all of which are time invariant. According to the John Multiplier Theorem (Section 4.5.1, p. 113), the necessary conditions for the minimum of I subject to the equality and inequality constraints are as follows  

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