Global stabilisation of a class of generalised cascaded systems by homogeneous method

ABSTRACT

This paper considers the problem of global stabilisation of a class of generalised cascaded systems. By using the extended adding a power integrator technique, a global controller is first constructed for the driving subsystem. Then based on the homogeneous properties and polynomial assumption, it is shown that the stabilisation of the driving subsystem implies the stabilisation of the overall cascaded system. Meanwhile, by properly choosing some control parameters, the global finite-time stability of the closed-loop cascaded system is also established. The proposed control method has several new features. First, the nonlinear cascaded systems considered in the paper are more general than the conventional ones, since the powers in the nominal part of the driving subsystem are not required to be restricted to ratios of positive odd numbers. Second, the proposed method has some flexible parameters which provide the possibility for designing continuously differentiable controllers for cascaded systems, while the existing designed controllers for such kind of cascaded systems are only continuous. Third, the homogenous and polynomial conditions adopted for the driven subsystem are easier to verify when compared with the matching conditions that are widely used previously. Furthermore, the efficiency of the proposed control method is validated by its application to finite-time tracking control of non-holonomic wheeled mobile robot.

KEYWORDS:

• Cascaded systems
• homogeneity
• adding a power integrator
• finite-time stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61573170]; the Zhejiang Open Foundation of the Most Important Subjects; the Postdoctoral Science Foundation of China [grant number 2015M571687]; the Australian Research Council [grant number DP120104986].