Parameter space mapping for linear discrete-time systems with parametric uncertainties

Many Parameter Space Approach (PSA) based methods have been proposed previously to determine the stabilizing controller parameter spaces for discrete-time systems. The PSA approach is based on sweeping over the whole range of singular frequencies which leads to an expensive numerical computation to find the boundaries of the stability region. These PSA based methods were used for obtaining the stability boundaries for parameter uncertain discrete-time systems as well. However, this results in extremely high computational complexity in addition to other drawbacks. In this study, an approach to determine the stabilizing controller parameter regions of linear discrete-time systems with uncertain parameters is proposed. This novel procedure makes use of the Strong Kharitonov theorem for getting over the high computational complexity resulted due to the uncertainty of the system. Moreover, the asserted approach utilizes a novel Lyapunov based mapping technique for avoiding the drawbacks accompanied with the previously presented PSA based methods in literature. Two different case studies are included in the paper to illustrate the advantages and effectiveness of the proposed method.