Search results for "Lyapunov functions"
showing 5 items of 5 documents
Robust reliable passive control of uncertain stochastic switched time-delay systems
2014
This paper investigates the problem of robust reliable passive control for a class of uncertain stochastic switched time-delay systems with actuator failures. The multiple Lyapunov functions (MLFs) technique is exploited to derive a delay-dependent sufficient condition for the stochastic switched time-delay systems to be passive and exponentially stable under a state-based switching law. Moreover, the proposed approach is extended to investigate stochastic switched systems with structured uncertainties. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.
Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits
2014
In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…
Lyapunov Functions for Second-Order Differential Inclusions: A Viability Approach
2001
AbstractIn this paper the existence of Lyapunov functions for second-order differential inclusions is analyzed by using the methodology of the Viability Theory. A necessary assumption on the initial states and sufficient conditions for the existence of local and global Lyapunov functions are obtained. An application is also provided.
The Egan problem on the pull-in range of type 2 PLLs
2021
In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …
Differential inclusions involving normal cones of nonregular sets in Hilbert spaces
2017
This thesis is dedicated to the study of differential inclusions involving normal cones of nonregular sets in Hilbert spaces. In particular, we are interested in the sweeping process and its variants. The sweeping process is a constrained differential inclusion involving normal cones which appears naturally in several applications such as elastoplasticity, electrical circuits, hysteresis, crowd motion, etc.This work is divided conceptually in three parts: Study of positively alpha-far sets, existence results for differential inclusions involving normal cones and characterizations of Lyapunov pairs for the sweeping process. In the first part (Chapter 2), we investigate the class of positivel…