Finite-Time Stabilization of Nonlinear Systems via Hybrid Control and Application to State Estimation of Complex Networks

Abstract

This paper investigates the problems of finite-time stabilization ( FTS) and finite-time contractive stabilization ( FTCS) for nonlinear systems by designing a novel class of hybrid control consisting of aperiodically intermittent control ( APIC) and impulsive control ( IC). Different from the single APIC, our proposed hybrid control specifically introduces IC on the intervals without control input in APIC. It shows that IC in hybrid control may not only flexibly shorten the length of the intervals with continuous control input, but also alleviate the design pressure of gain of APIC. Based on the hybrid control, some Lyapunov-based criteria are derived to guarantee the FTS and FTCS, where a potential relationship between system structure, APIC law, and impulse actions is established. Specifically, some linear matrix inequalities ( LMIs) based criteria are presented to design the hybrid control gains. As an application, the theoretical results are extended to the finite-time state estimation of complex networks involving the unavailable network states. With the available measurement outputs, the hybrid state estimator involving both APIC and IC is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of our results. Note to Practitioners-Unlike the Lyapunov stability results, the transient performances described by FTS and FTCS can be quantitatively guaranteed in the finite-time sense and have better applicability for the practical engineering requirements. This paper was motivated to solve FTS and FTCS problems. To guarantee the FTS and FTCS, a novel class of hybrid control is designed, which integrates the advantages of APIC and IC. Compared with the single APIC, the introduction of IC may reduce the dependence on the continuous control input in APIC, which significantly reduces the energy consumption of communication. The introduction of IC can also alleviate the design pressure of APIC to some extent. Hence, some easy-checked FTS and FTCS criteria are presented based on the proposed hybrid control. In practical applications, the theoretical results are extended to investigate the finite-time state estimation of complex networks considering unavailable network states. Utilizing the available measurement outputs, the corresponding hybrid state estimator consisting of APIC and IC is constructed. Finally, note that the impulsive transmission of ball motion is considered to further illustrate the practicability of our proposed results. In the future work, our proposed hybrid control strategy can be applied in other practical projects, such as the finite-time control of omnidirectional mobile robot.