Feedback control of nonlinear discrete-time systems based on observers (Q2726006)

A new kind of simple and easily implementable state observers are proposed for a class of nonlinear discrete-time systems: NEWLINE\[NEWLINE\Sigma:\begin{cases} x(k+1)=f(x(k),u(k))\\ y(k)=h(x(k)),\end{cases}NEWLINE\]NEWLINE where \(x(k)\in\mathbb R^n\) is state; \(u(k)\in\mathbb R\) is controlled state; \(y(k)\in\mathbb R\) is output; \(f:\mathbb R^n\times \mathbb R\to\mathbb R^n\), \(h:\mathbb R^n\to\mathbb R\), \(f(0,0)=0\), \(h(0)=0\). The convergence of the estimated state towards the true state is proved. The observer-based controllers stabilizing the systems are designed. A numerical example is given to demonstrate effectiveness of the proposed method.