Saturated stabilization of feed‐forward systems subject to lower‐order perturbations

• Published in: International journal of robust and nonlinear control Vol. 34; no. 12; pp. 8248 - 8271
• Main Authors: Liu, Jun, Ye, Huawen, Chen, Zilong
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.08.2024
• Subjects: common Lyapunov function; Liapunov functions; Perturbation; row‐diagonally dominant estimates; saturated control; Stability; Stabilization; System theory; Systems theory
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7387

This article revisits saturated stabilization of the feed‐forward systems that are subject to lower‐order perturbations, with the purpose of providing new analysis approaches. To carry out the saturation reduction analysis, we do not use the existing time‐interval based contradiction approach, but propose a Lyapunov function method; to deal with the reduced system (the closed‐loop system that does not contain saturation any longer), we do not use the “adding a power integrator” backstepping scheme, but propose an approach which is established by jointly using the vector Lyapunov function theory, a matrix measure stability theory and the switching systems theory. As a result, a quite number of inequality computations can be avoided, and the stability conditions summarized in two analysis procedures can be expressed by directly using the system parameters. This article also shows that the established approaches are applicable to the uncertain feedforward systems subject to linear input perturbation and consequently, allows to present new stabilizing control laws for several intractable under‐actuated systems.