Observer-Based Local Stabilization of State-Delayed Quasi-One-Sided Lipschitz Systems with Actuator Saturation

This paper addresses the problem of asymptotic stabilization for a class of systems composed of linear and nonlinear parts, both of which are affected by a common state delay that increases the complexity of the dynamics. Within this class of systems, the nonlinear component depends on unmeasurable states and satisfies a quasi-one-sided Lipschitz (QL) condition, which allows for tractable analysis. Moreover, the control input is subject to saturation, further complicating the stabilization task. The proposed remedy involves three key components: an observer to estimate the unmeasurable states, a Lyapunov–Krasovskii (LK) functional to handle the delay, and a dead-zone model to represent the saturation nonlinearity. This combined approach allows for the derivation of sufficient conditions that ensure the local asymptotic stabilization of an augmented system comprising the state and the estimation error. Furthermore, the domain of attraction is estimated. The obtained conditions are not LMIs. This arises from a shared matrix variable that is required to simultaneously verify the weak QL Lipschitz condition and appear within the LK functional, creating a nonlinear coupling. In the existing literature, this matrix is typically fixed and not treated as a decision variable to simplify the problem. In contrast, this work proposes a novel approach by employing an appropriate decoupling technique, which allows this matrix to remain a decision variable and provides greater flexibility in the design. To validate the proposed design, we provide a numerical simulation.