A Lyapunov Functional Approach to Robust Stability Analysis of Continuous-Time Uncertain Linear Systems in Polytopic Domains

作者：Lee Dong Hwan; Tak Myung Hwan; Joo Young Loon^*

来源：International Journal of Control Automation and Systems, 2013, 11(3): 460-469.

DOI：10.1007/s12555-012-0426-1

• Complex functions
• linear matrix inequality
• linear time-invariant systems
• relaxation
• robust stability

In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.

• 出版日期2013-6