Robust decentralised stabilisation of interval discrete-time singular large-scale systems

The problem of robust decentralised state-feedback stabilisation for discrete-time singular large-scale systems with interval uncertainties is addressed in this study. By using the matrix norm operation and the rank-1 matrix technique for interval matrices, two sufficient conditions to check the robust decentralised stabilisability of uncertain discrete-time singular large-scale systems are, respectively, obtained. At the expense of problem size (numerical complexity), the second condition gives a less conservative result than the first one. It is therefore reasonable to check the robust stabilisability by the first condition, and then if it fails, resort to the second one. Finally, illustrative examples show that the proposed conditions are effective for the design of robust decentralised stabilising state-feedback controller for not only the uncertain discrete-time singular large-scale systems but also the uncertain discrete-time regular large-scale systems.