Separation principle for discrete‐time quasi‐one‐sided Lipschitz nonlinear systems

Abstract This paper is concerned with output stabilisation for a class of discrete‐time quasi‐one‐sided Lipschitz nonlinear systems. Firstly, an observer is designed for estimating the state of the systems in terms of quasi‐one‐sided Lipschitz condition and quadratic inner‐boundness condition. Then, a state feedback controller is proposed to stabilize the systems. Subsequently, it is shown that the separation principle holds for stabilisation of the discrete‐time nonlinear systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, the state observer and feedback controller can be designed separately, even though the parameter (A,B) of discrete‐time systems is not stabilisable and parameter (A,C) is not detectable. Finally, two numerical examples are given to indicate the feasibility of the main results