This chapter focuses on the analysis and the control structure design on the ALSTOM gasifier system. The difficulties in the ALSTOM gasifier problem are the high-order system, highly coupled in the inputs and outputs, and the numerically poor linear models that affects the control system design process. ALSTOM gasifier is a nonlinear multivariable system, having four outputs to be controlled with a high degree of cross coupling between them. The concept of the linear quadratic regulator (LQR), or commonly known as optimal state-feedback design, uses a set of weighting matrices to penalize the states and control inputs of the system. LQR designed controllers ensure good stability margin and sensitivity properties. The weighting function is selected to shape the sensitivity and the input sensitivity of the system to the required bandwidth and the upper and lower bounds. The chapter discusses the methods that are used to compare the various controllers designed.