Output tracking for a class of nonlinear time-varying systems based on state observers (Q2705711)

The authors consider output tracking for a class of affine nonlinear time-varying systems modeled by equations of the form: NEWLINE\[NEWLINE\dot x=f(x,t)+g(x,t)u, \qquad y=h(x,t),NEWLINE\]NEWLINE where \(x\in\mathbb R^n\) is the state, \(u\), \(y\in\mathbb R^m\) are the control input and the measured output, respectively, \(f(x,t)\), \(g(x,t)\) and \(h(x,t)\) are known sufficiently smooth matrix functions with appropriate dimensions, \(\forall x\in\mathbb R^n\), \(\forall t\in\mathbb R^+\), \(f(0,t)=0\), \(h(0,t)=0\), \(g(x,t)\neq 0.\) A kind of observer is presented for the systems. The observer-based controllers which are used to track the desired signals are designed, and the exponential stability for the closed-loop systems is proved. Remarkably, the controllers and observers can be designed independently. An example is given to demonstrate the effectiveness of the proposed approach.