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

Graziano Chesi
2010 2010 3rd International Symposium on Systems and Control in Aeronautics and Astronautics  
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 homo geneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). Moreover, it
more » ... 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. G. Chesi is with the
doi:10.1109/isscaa.2010.5633207 fatcat:eq5oqemaufbijajzsrfq24uw5q