Comparisons among robust stability criteria for linear systems with affine parameter uncertainties

This paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems, where the system state matrices considered are affinely dependent on the uncertain parameters. At first, a robust stability criterion for the class of systems to be affinely quadratically stable (AQS) is derived based on the vertex separator approach, where affine parameter-dependent Lyapunov functions are exploited to prove stability. Then comparison results between the robust stability criterion and the existing tests for AQS are given in terms of degree of conservatism. A numerical example is given to illustrate the results.