Affine parameter-dependent Lyapunov functions for real parametric uncertainty

A new test of robust stability/performance is proposed for linear systems with uncertain real parameters. This test is an extension of the notion of quadratic stability where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to an linear matrix inequality (LMI) problem, hence is numerically tractable. This LMI-based test can be used for both fixed or time-varying uncertain parameters and is always less conservative than the quadratic stability test whenever the parameters cannot vary arbitrarily fast. Its also completely bypasses the frequency sweep required in real μ-analysis