Parameter-dependent Lyapunov Functions for Real Parametric Uncertainty

A new test of robust stability/performance is proposed for linear systems with uncertain real-valued parameters. This test is an extension of the notion of quadratic stability where the xed quadratic Lyapunov function is replaced by a Lyapunov function with aane dependence on the uncertain parameters. Admittedly with some conservatism , the construction of such parameter-dependent Lyapunov functions can be reduced to an LMI problem, hence is numerically tractable. This LMI-based test can be used for both xed or time-varying uncertain parameters and is always less conservative than the quadratic stability test whenever the parameters cannot vary arbitrarily fast. It is also less conservative than the real upper bound for time-varying parameters, and several examples demonstrate that it compares advantageously with this upper bound even for xed parameters.