Dwell-time-based stabilization of switched linear singular systems with all unstable-mode subsystems

Abstract

The global stabilization design of a class of switched linear singular systems via a novel dwell-time switching is investigated and solved in this work. The distinguishing feature of the proposed method is that stability of all subsystems of the switched systems is not necessarily required. A time-varying coordinate transformation is introduced first in order to convert the problem into an equivalent one of reduced-order switched conventional linear system with state jumps. Then, by constructing certain new multiple time-varying Lyapunov functions, computable sufficient conditions for the global stabilization task are proposed within the framework of dwell-time switching. Given the assumed instability of individual subsystems, the stabilization of the switched system is achieved under the condition of confining the dwell time by a certain pair of upper and lower bounds, which restrict the growth of Lyapunov function for the actively operating subsystem, thus decrease the energy of the Lyapunov function of the overall switched system at switching times. In addition, the multiple time-varying Lyapunov functions method is also used to analyze the stability analysis of a class of switched linear singular systems with stable subsystems. Two illustrative examples are presented to demonstrate the effectiveness of the proposed method.