Stability of switched linear discrete-time descriptor systems with explicit calculation of a common quadratic Lyapunov sequence

In this paper, the stability of a switched linear regular descriptor system is considered. It will be shown that if a certain simultaneous triangularization condition on the subsystems is fulfilled and all the subsystems are stable then the switched system is stable under arbitrary switching. The result involves different descriptor matrices and extends to the singular case well-known results from the standard one. Furthermore, an explicit construction of a common Lyapunov sequence for a set of discrete-time regular linear descriptor subsystems is performed. The main novelty of the proposed approach is that the common Lyapunov sequence can be easily computed in comparison with previous works which either presented computationally-demanding methods or did not construct the common Lyapunov sequence explicitly.