Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

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

“…Being aware of the above obstacles, a new approach is subtly developed in this paper. Compared with the existing works [24,[26][27][28][29][30][31][32][33], the main contributions of this paper can be summarized from two aspects: (i) This paper is focused on the problem of fixed-time stabilization for time-varying second-order multivariable nonlinear systems; thus, compared with the existing results concerning scalar systems or single input systems (e.g., [24,[26][27][28][29][30]), we offer a novel insight on how to tackle the problem of fixed-time stabilization for a more general class of nonlinear systems. (ii) By introducing extra manipulations in the feedback domination, the technique of adding a power integrator [34] is skillfully revamped to develop a distinctive approach to the synthesis of a fixed-time stabilizer together with a Lyapunov function which is significantly important for verifying fixed-time convergence and stability.…”

“…In other words, by fixed-time controller design, a predetermined bound of the settling time (function) can be accordingly assigned. Particularly, the fixed-time stabilization is very promising, especially when the organized controller is assigned intentionally to achieve certain control precision in a desired time interval [23,25,26]. Realizing this feature, research study has been more recently focused on the fixed-time stabilization of various nonlinear systems, for instance, high-order regulators [27], multi-agent systems [28,29], power systems [30], etc.…”

“…To the best of our knowledge, most of the existing studies on fixed-time stabilization are essentially concerned with scalar systems or single input control structures [24,[26][27][28][29][30]. For multivariable multi-input systems, very few results are available in the literature; see, for example, [31][32][33], in which the fixed-time stabilization of time-invariant linear and nonlinear systems are addressed, respectively.…”

Global Prescribed-Time Controller Design for p-Normal Switched Nonlinear Systems With Dead-Zone Inputs

“…Under the new framework of fixed-time stability, various works have appeared to address control designs of linear/nonlinear systems. Roughly, the existing approaches on such control designs can be classified into two classes: the bi-limit homogeneous approach [30,31] and the Lyapunov-based approach [32][33][34][35][36][37][38]. It is worth pointing out that, in the bi-limit homogeneous approach, the upper bound of the settling time II, the problem formulation and preliminaries of this paper are introduced.…”

Pth moment input-to-state stability of stochastic impulsive switched delayed systems

“…For example, observer-based robust finite time H ∞ sliding mode control problem was analyzed for switching systems (Gao et al, 2016). In Gao et al (2019), global fixed-time stabilization for a class of switched nonlinear systems was studied. For a special Markov switched system, stability analysis and control issues for Markovian jump systems are investigated, respectively (Shen et al, 2018a,b; Yan et al, 2015, 2018; Yao et al, 2018; Zuo et al, 2018).…”