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In linear systems, it is well known that any combination of stabilizing state feedback controller and a state observer results in the output feedback controller which asymptotically stabilizes the closed-loop system. This is known as the separation principle, which does not generally hold for nonlinear systems. For nonlinear systems, the output feedback problem is usually pursued by extending the results of observer synthesis, which itself is a challenging problem. In this paper, we investigate the stabilization via an observer configuration problem for some classes of nonlinear time-varying systems by using new integral inequalities of Gronwall type. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed practical observer will achieve the global practical exponential stabilization. Furthermore, the effectiveness of the proposed scheme is shown through simulation for two numerical examples.

<p style='text-indent:20px;'>This paper addresses input-to-state stability (ISS) and integral input-to-state stability (iISS) for non-autonomous infinite-dimensional control systems. With the notion of uniformly exponential stability scalar function, ISS and iISS are considered based on indefinite Lyapunov functions. In addition, we obtain several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities. As a result, the iISS criteria of non-autonomous bilinear systems is also established. Furthermore, an illustrative example is given to show the applicability of the results.</p>