# Stability proof of nominal MPC with terminal cost and constraint

While going trough these slides, I wasn't able to make sense of the following on slide 32: (if only providing the url to the slides is not ok I will edit the question, but doing it like that saves a lot of time)

Why does the fact that $V_f$ is a Lyapunov function result in $$V_f(\tilde{x}_{N+1}) − V_f(x_N) + l(x_N, κ_f(x_N))\leq 0?$$

• Can you add a summary, because slide 32 alone does not give any context for the mentioned variables. Sep 3 '18 at 12:43