Unmanned Aerial Vehicles (UAVs) are increasingly deployed in safety–critical missions that demand advanced control strategies capable of addressing nonlinear dynamics, stringent constraints, and uncertain environments. Model Predictive Control (MPC) has emerged as a powerful framework for these challenges, yet its finite-horizon nature requires additional stabilizing mechanisms to ensure reliable closed-loop performance. Among the existing stabilizing strategies, Lyapunov-based MPC has attracted significant attention for embedding explicit stability conditions into the optimization problem, providing a flexible and computationally efficient alternative to terminal-ingredient formulations. This paper provides a comprehensive survey of Lyapunov-based MPC for UAVs, examining its stabilizing mechanism and tracing its evolution from a theoretical tool to a practical framework. The survey classifies existing contributions according to control tasks, modeling fidelity, system architectures, stability assurance mechanisms, and validation strategies. Beyond a descriptive review, the survey critically analyzes fundamental limitations and deployment bottlenecks related to conservatism, assumptions, and real-time implementation. Finally, key research directions are outlined, focusing on reducing conservatism, improving scalability, enhancing robustness, and strengthening implementation-aware validation. These findings position Lyapunov-based MPC as a promising framework for next-generation UAV autonomy.

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time (PDT) constraint. A double-clock-dependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system, and assign to each system a controller scheduled by a clock. A necessary and sufficient convex stability criterion is presented for the nominal system, and is further extended to the stabilization controller design with a nominal clock. In the presence of bounded peak disturbances, another stabilization controller with an error clock is developed for the error system, with the purpose of “minimizing” the reachable set of the error system by the ellipsoidal techniques. It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system, i.e., a union of a family of bounding ellipsoids, that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system. Two numerical examples are provided to verify the effectiveness of the developed results.

In this paper, we focus on the robust output feedback Model Predictive Control (MPC) design for linear constrained Networked Control Systems (NCSs) subject to disturbances, observation noise and random packet dropouts in both Sensor-Controller (S-C) and Controller-Actuator (C-A) channels. The proposed control scheme consists of an observer to estimate the state and a robust model predictive controller to stabilize the disturbed system. In the observer design, we extend the Luenberger observer to estimate the state in two communication scenarios. The resulting dynamics of estimation error can be described by a switched system. With this, a Generalized Robust Positive Invariant (GRPI) set can be developed, providing an explicit bound of estimation errors in the presence of admissible disturbances and packet dropouts. Similarly, a GRPI set is established to bound the prediction error in the MPC framework under the proposed state estimator. These two GRPI sets are further used to develop tightened constraints in the proposed robust output feedback MPC scheme to ensure robust constraint satisfaction. It is rigorously proved that the proposed robust MPC algorithm is recursively feasible and the system state converges to a compact set around the origin. Finally, simulation results are provided to verify the effectiveness of the proposed robust output feedback MPC scheme.

Switched systems play an imperative role in modeling many real industrial systems with abrupt changes. Due to possible exposure to unreliable and complex physical environments, switching dynamics may simultaneously face multiple faults, including the unexpected controller disconnect, the temporary mismatch between subsystems and desired corresponding controllers, and the intermittent disordering of mode transitions. These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution, thereby bringing significant yet challenging issues to be tackled. This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time (MDT). From a set-theory perspective, we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties. Moreover, the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof. A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.