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This paper illustrates the performance of three different controller designs on a 2nd order simplified nonlinear engine vehicle dynamical model. The nonlinear error model is generated around a desired constant equilibrium point where dynamic behavior lies in the convex hull of a set of polytopes. The necessary theory for quadratic stability and various constraints for a feedback control are set forth and formulated as linear matrix inequalities (LMIs). Tradeoffs considered in the designs are convergence speed of state trajectories and fuel economy. Three distinct optimizations are considered. The control performance for each design is simulated to show the design tradeoffs.