Bi-quadratic stability of uncertain linear systems

Deals with the problem of robust stability of linear systems with uncertain real time-varying parameters with magnitudes and rates of change (or variations, in discrete-time) which are confined to a given convex region. A notion of robust stability, referred to as bi-quadratic stability, which is based on a Lyapunov function that depends quadratically on the uncertain parameters is proposed. LMI based sufficient conditions for bi-quadratic stability of continuous- and discrete-time systems are developed. The proposed stability analysis methods have the advantage that they can be used for solving problems of robust control synthesis, including robust stabilization, robust H₂ control, and robust H_∞ control