Finite‐time stabilisation for a class of nonlinear descriptor systems

Finite-Time Stabilization for a Class of Nonlinear Singular Systems

“…Here, we slightly abuse the notation of x(t) and x without confusedness, and the notations of A(x(t)), B(x(t)) are simplified as A(x) and B(x) respectively. Motivated by the work of [23], [24], the following definition is given. Definition 1.…”

“…Based on those results, the finite-time control problem was also considered for nonlinear singular systems with interval timevarying delay [21] and nonlinear singular Markovian systems with sensor fault [22]. When the nonlinear function was not restricted to satisfy the Lipschitz condition, the finite-time stabilization problem for affine nonlinear singular systems was considered in the discrete-time [17] and continuous-time [23] contexts respectively.…”

“…We revisit the finite-time stabilization problem for a class of nonlinear singular systems in this paper. This problem was first considered in [23], where some sufficient conditions were given for the considered nonlinear singular system to be stabilizable, H ∞ stabilizable, and adaptive H ∞ stabilizable. However, simple mathematical verifications show that the proposed sufficient conditions are not correct.…”

Robust Finite-Time Stabilization for Uncertain Discrete-Time Linear Singular Systems

“…For example, the finite-time stabilization problem of linear singular systems subject to parametric uncertainty and disturbances was studied in [11], where some fundamental definitions for state-space linear systems were extended to singular linear systems, and the finite-time H ∞ stabilization problem for linear singular systems with parameter uncertainty was studied in [12]. The finite-time dissipative control problem for singular Markovian jump time-delay systems was studied in [13], where the time-varying transition rate and actuator saturation were considered. The finite-time observer design problem was considered recently for a class of singular systems subject to unknown inputs in both the state and the output equations in [14], where some linear matrix inequality results were given.…”

Parametric Control to a Type of Descriptor Quasi-Linear Systems via Output Feedback

“…Wu et al discuss the stabilization problem of nonlinear descriptor systems with delay and give a sufficient condition of existence and uniqueness for the solution to descriptor nonlinear systems according to LMI approach [17]. In addition, there are also other results for descriptor nonlinear systems (see [18]- [22] and other relative references).…”