Lyapunov-based stability region computation approach

For the design of controllers, D-decomposition techniques like the Parameter Space Approach (PSA) are widely used to identify the space of stabilizing controller parameters. The PSA approach is based on sweeping over the entire range of singular frequencies which leads to an expensive numerical computation and a waste of time to obtain the boundaries of the stability region. Two novel methods are proposed in this paper to obtain the stability region by using Lyapunov stability criterion. This paper focuses on the state-feedback controller design. Thus, the classical widely-used Parameter Space Approach is presented first. Following this, the newly proposed Lyapunov based methods are discussed. The difference between both methods is shown by examples which demonstrate that the novel approach is applicable for a big variety of different system structures and it has a less complex computation routine.