Generalisation of the Perron–Frobenius theory to matrix pencils

AbstractWe present a new extension of the well-known Perron–Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not satisfied

Structural Identifiability of Linear Singular Dynamic Systems

[EN] Structured singular systems depending on a parametric vector are considered. The identification of the parameters is analyzed in terms of the input-output behavior of the system. The role of the reachability and observability properties in this analysis is studied and a characterization of the structural identifiability property is given. Finally, the structural identifiability of a positive reachable system is studied.Supported by Spanish DGI grant MMT2007-64477Cantó Colomina, B.; Coll, C.; Sánchez, E. (2009). Structural Identifiability of Linear Singular Systems. Lecture Notes in Control and Information Sciences. 389:243-249. https://doi.org/10.1007/978-3-642-02894-6_23S243249389Audoly, S., D’Angió, L., Saccomani, M.P., Cobelli, C.: Global identifiability of linear compartmental models. IEEE Trans. Biomed. Eng. 45, 36–47 (1998)Ben-Zvi, A., McLellan, P.J., McAuley, K.B.: Identifiability of linear time-invariant differential-algebraic systems. I. The generalized Markov parameter approach. Ind. Eng. Chem. Res. 42, 6607–6618 (2003)Bru, R., Coll, C., Romero, S., Sánchez, E.: Some problems about structural properties of positive descriptor systems. LNCIS, vol. 294, pp. 233–240. Springer, Heidelberg (2003)Bru, R., Coll, C., Sánchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra and its Applications 349, 1–10 (2002)Dai, L.: Singular Control Systems. LNCIS, vol. 118. Springer, Heidelberg (1989)Dion, J.M., Commault, C., Van der Woude, J.: Generic properties and control of linear structured systems: a survey. Automatica 39, 1125–1144 (2003)Miyamura, A., Kazuyuki, K.: Identifiability of delayed singular systems. In: Proceedings 5th Asian Control Conference, Melbourne, Australia, pp. 789–797 (2004)Tayakout-Fayolle, M., Jolimaitre, E., Jallut, C.: Consequence of strutural identifiability properties on state model formulation for linear inverse chromatography. Chemical Eng. Science 55, 2945–2956 (2000