In this chapter it is explained the construction of robust control Lyapunov functions. This chapter begins with the definition of robust stability and robust performance for linear and nonlinear dynamic systems in order to obtain the robust requirements to measure this index in order to ensure the best performance of the closed loop robust system. Then the construction of robust control for linear and nonlinear systems is explained in order to define the theoretical conditions for the robust control system design. One of the main contributions of this book chapter is that the robust stability conditions and robust performance are extended to the discrete time case, something that is very limited reported in the literature and that this book chapter provides a novel contribution to the field. Besides, the derivation of control laws for the continuous and discrete time cases is presented, in order to provide the reader the mathematical background to design controllers for this kind of systems. Another important contribution of this book chapter is that the derivation of optimal robust control laws is presented, in specific the design of optimal robust linear quadratic regulators for the continuous time case. Finally, illustrative examples are presented to elucidate the experimental results of this research study in order to obtain the optimal closed loop system performance.