ABSTRACT
In the previous chapter, adaptive control of a class of nonlinear systems in discretetime was presented using neural networks. Although Lyapunov stability analysis and passivity properties were detailed, the analysis was limited to a specific class of nonlinear systems of the form x(k + 1) = f(x(k)) + u(k), where there are no uncertainties in the coefficient of the control input u(k). However, if a system in continuous-time of the form ẋ = f 1(x) + u(k) is discretized (Chen and Khalil 1995), the system in discrete-time will be of the form x(k + 1) = f(x(k)) + g(x(k))u(k) for some functions f(.) and g(.). Therefore,, in this chapter the results in the previous chapter are extended to the more general class of nonlinear discrete-time systems of the form x(k + 1) = f(x(k)) + g(x(k))u(k).
