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On the robust stability of continuous-time and discrete-time time-invariant uncertain systems with rational dependence on the uncertainty: A non-conservative condition

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1 Author(s)
Chesi, G. ; Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong, China

A key problem in automatic control consists of investigating robust stability of systems with uncertainty. This paper considers linear systems with rational dependence on time-invariant uncertainties constrained in the simplex. It is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem constructed through homogeneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). Moreover, it is shown that this condition is also necessary for establishing either stability or instability by using a sufficiently large degree of the HPD-QLF. Some numerical examples illustrate the use of the proposed approach in both cases of continuous-time and discrete-time uncertain systems.

Published in:

Systems and Control in Aeronautics and Astronautics (ISSCAA), 2010 3rd International Symposium on

Date of Conference:

8-10 June 2010