Robust performance analysis of linear time-invariant parameter-dependent systems using higher-order Lyapunov functions

This paper studies the robust stability/performance analysis of linear time-invariant parameter-dependent systems for which the coefficient matrices in the state-space representations are parameter-dependent in negative as well as positive power series of parameters, and whose parameters are supposed to lie in a given convex region. To analyze the robust stability/performance, we use parameter-dependent Lyapunov functions that are parameter-dependent in negative as well as positive power series, and derive sufficient conditions for them via parametrically affine linear matrix inequalities. Although our formulae have greater numerical complexity than previous works, they encompass formulae based on biquadratic stability, which has been proposed to obtain less conservative conditions, and conventional quadratic stability. We present numerical examples that demonstrate the effectiveness of our proposed methods compared with existing methods.