Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays
- 1 June 2008
- journal article
- research article
- Published by Informa UK Limited in International Journal of Control
- Vol. 81 (6), 865-882
- https://doi.org/10.1080/00207170701261986
Abstract
This paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays. A sufficient condition, which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient, is established in terms of the linear matrix inequality (LMI) technique and a new Lyapunov–Krasovskii functional. The estimating procedure is implemented by solving a set of LMIs, which can be checked easily by effective algorithms. Under the proposed condition, the algebraic subsystems possess the same decay rate as the differential ones. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.Keywords
This publication has 27 references indexed in Scilit:
- New Exponential Estimates for Time-Delay SystemsIEEE Transactions on Automatic Control, 2006
- Exponential estimates for neutral time delay systems with multiple delaysInternational Journal of Robust and Nonlinear Control, 2005
- Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delaysOptimal Control Applications and Methods, 2005
- Robust$H_infty$Filter Design of Uncertain Descriptor Systems with Discrete and Distributed DelaysIEEE Transactions on Signal Processing, 2004
- Robust H∞ control for uncertain singular systems with state delayInternational Journal of Robust and Nonlinear Control, 2003
- Exponential stability of stochastic delay interval systems with Markovian switchingIEEE Transactions on Automatic Control, 2002
- On an estimate of the decay rate for applications of Razumikhin-type theoremsIEEE Transactions on Automatic Control, 1998
- Robust stability criteria for dynamical systems including delayed perturbationsIEEE Transactions on Automatic Control, 1995
- Delay independent stability conditions and decay estimates for time-varying functional differential equationsIEEE Transactions on Automatic Control, 1994
- Further comments on ‘Comments on “On an estimate of the decay rate for stable linear delay systems”’International Journal of Control, 1986