Cart (Loading....) | Create Account
Close category search window

Necessary and Sufficient LMI Conditions for Stability and Performance Analysis of 2-D Mixed Continuous-Discrete-Time Systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

The purchase and pricing options are temporarily unavailable. Please try again later.
2 Author(s)
Chesi, G. ; Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong, China ; Middleton, R.H.

This paper proposes necessary and sufficient conditions for stability and performance analysis of 2-D mixed continuous-discrete-time systems that can be checked with convex optimization, in particular linear matrix inequalities (LMIs). Specifically, the first contribution of the paper is a condition for exponential stability based on the introduction of a complex Lyapunov function depending polynomially on a parameter and on the use of the Gram matrix method. It is shown that this condition is sufficient for any chosen degree of the complex Lyapunov function, and necessary for an a priori known degree. The second contribution is a non-Lyapunov condition for exponential stability based on eigenvalue products. This condition is necessary and sufficient, and has the advantage of requiring a significantly smaller computational burden for achieving necessity. Lastly, the third contribution is to show how upper bounds on the H∞ norm of 2-D mixed continuous-discrete-time systems can be obtained through a semidefinite program based on complex Lyapunov functions. A necessary and sufficient condition is provided for establishing the tightness of the found upper bounds.

Published in:

Automatic Control, IEEE Transactions on  (Volume:59 ,  Issue: 4 )

Date of Publication:

April 2014

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.