Prescribed Finite-Time <i>H</i> <sub>∞</sub> Control for Nonlinear Descriptor Systems
Xiaodong Lü, Haitao Li
Abstract
In this brief, the prescribed finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> problems of nonlinear descriptor systems (NDSs) with and without actuator saturation are respectively investigated. When addressing this problem of NDSs subject to actuator saturation, it is pointed out that the existing treatments for the saturation nonlinearities are not so effective. The reason is that some of them cannot ensure that the resulting closed-loop systems are impulse controllable, and others cannot make sure that the closed-loop system can achieve prescribed finite-time stable. To overcome this issue, an available and interesting treatment is proposed. The main characteristic of this treatment is that the saturation nonlinearity is decomposed into a linear form consisting of the control signal and its constant constraints. Based on this treatment, the state feedback scheme is adopted for the considered problem, and some sufficient conditions are obtained. To illustrate the efficiency of the proposed results, an example about circuit systems is provided.