A Hybrid Control Approach to $H_{\infty }$ Problem of Nonlinear Descriptor Systems With Actuator Saturation
Xiaodong Lü, Haitao Li
Abstract
In this article, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> problem of nonlinear descriptor systems (NDSs) is investigated. For regular or nondescriptor systems, this problem can be solved via the event-triggered control law. But this control law may be ineffective for the same problem of descriptor systems. The reason is that the discontinuity of the event-triggered controller will cause sudden failure of the algegbraic part of descriptor systems at each triggering instant. From the perspective of mathematics, the algebraic equation will have no solution at each triggering instant. To address this problem, a novel hybrid control scheme is introduced. The main characteristic of this control scheme is that it consists of an event-triggered controller and an impulsive controller. It is shown that the impulsive controller plays an extremely important role in adjusting system states to satisfy the algebraic equation. Based on this hybrid control scheme, some improved results are proposed compared with the existing ones. Finally, an example about circuit systems is given to illustrate the effectiveness of the results.