A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint

Output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint

“…On the basis of Definition 1, the next lemma characterizes the implication of a BLF for a time‐varying system, and its proof can be found in our previous work 29 …”

“…Despite the significant advances in pure stabilization, relatively less progress has been made 25‐29 toward addressing the problem of asymptotic stabilization for high‐order nonlinear systems subjected to pre‐specified output constraints, which are necessarily and inevitably imposed on the system outputs due to safety considerations and/or performance specifications 30‐35 . The key treatment presented in References 25‐29 for addressing the stabilization problem with output constraints is the utilization of a barrier Lyapunov function (BLF) (see References 29 and 36 for the definition) along with the critical assumption of full‐state availability, namely, only the state feedback design is considered in References 25‐29. Notably, if full‐state measurements are not available, the methods in References 25‐29 are no longer workable, and the development of a new scheme on the basis of output feedback design is surely imperative.…”

“…The key treatment presented in References 25‐29 for addressing the stabilization problem with output constraints is the utilization of a barrier Lyapunov function (BLF) (see References 29 and 36 for the definition) along with the critical assumption of full‐state availability, namely, only the state feedback design is considered in References 25‐29. Notably, if full‐state measurements are not available, the methods in References 25‐29 are no longer workable, and the development of a new scheme on the basis of output feedback design is surely imperative. To the best of our knowledge, the problem of output feedback stabilization for high‐order nonlinear systems ( p ‐normal form systems) with output constraints has never been investigated or solved in the literature, even in the two‐dimensional case.…”

Output feedback stabilization within prescribed finite time of asymmetric time‐varying constrained nonholonomic systems

“…39,40 In recent years, drew by the practical demands, the control design of constrained systems has attracted increasing attention. [41][42][43][44][45][46][47][48] However, to the author's knowledge, there are few results on the fixed-time stabilization of state/output-constrained nonholonomic systems reported in the literature except References 49 and 50, where the different state feedback constrained control schemes are presented to achieve the stabilization task. Note that the control schemes proposed in References 49 and 50 are essentially builded on the information of entire system state, which will render they are invalid to the case of only partial-state information available.…”

A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

“…Compared to asymptotic stabilization, which means that the convergence rate is, at best, exponential with infinite settling time [6,7], finite-time stabilization is more attractive as the systems with finite-time convergence usually demonstrate some superior properties, such as faster convergence, high accuracies, and better robustness to uncertainties, and/or external disturbances [7][8][9][10][11], which are rather important for demanding applications. Being aware of these advantages, the finite-time stabilization problem has been intensively studied for nonlinear systems, and numerous interesting results have been obtained in the past decades (see, e.g., [12][13][14][15][16][17][18][19][20][21]). Among the existing results, owing to its benefits including fast response and easy implementation, the terminal sliding mode control [20], together with its nonsingular modification [21], has been extensively recognized as one of the most popular/effective approaches for finite-time stabilization.…”