access icon free Drazin inverse conditions for positivity and stability of switched descriptor systems

This study provides an alternative approach to stability analysis of positive switched descriptor systems (SDSs). First, by introducing a Drazin-inverse-based projector which takes a simpler form than the traditional matrix-decomposition-based ones, the state consistency of SDSs is guaranteed. Then, regarding the fact that SDSs may not be positive even if all individual subsystems are positive, two different definitions of positivity are introduced and a complete characterisation is provided. The stability issue is also addressed and two checkable approaches are proposed, which are formulated as a set of linear matrix inequality problems and linear programming problems, respectively.

Inspec keywords: linear systems; matrix algebra; stability; linear programming; control system synthesis; linear matrix inequalities; time-varying systems

Other keywords: linear matrix inequality problems; Drazin inverse conditions; positive switched descriptor systems; individual subsystems; traditional matrix-decomposition-based ones; simpler form; Drazin-inverse-based projector; stability analysis; SDSs; checkable approaches; stability issue; state consistency

Subjects: Control system analysis and synthesis methods; Stability in control theory; Linear control systems; Linear algebra (numerical analysis); Algebra

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