Discrete-time nonlinear analysis and feedback control with nonquadratic performance criteria

In this paper we develop a unified framework to address the problem of discrete-time optimal nonlinear analysis and feedback control. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the discrete-time Bellman equation thus guaranteeing both stability and optimality. The overall framework provides the foundation for extending discrete-time linearquadratic controller synthesis to nonlinear-nonquadratic problems.