Regularisation and stabilisation of linear discrete-time descriptor systems [Brief Paper]

The regularisation (to make the closed-loop system regular and causal) and stabilisation problems of linear discrete-time descriptor systems are addressed in this study. If the state of a descriptor system is divided into the regular and singular substates, the regularisation and stabilisation can be achieved by singular substate feedback and regular substate feedback, respectively. Therefore a simultaneous regularisation and stabilisation problem can be solved by a two-step procedure. LMI-based necessary and sufficient conditions for the regularisability via singular substate feedback and the stabilisability via regular substate feedback are established for the first and second steps, respectively. Finally, the proposed results are also extended to the robust regularisation and stabilisation of linear discrete-time descriptor systems with norm-bounded uncertainties.