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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

2 Kaczorek T.

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Strong stability of positive and compartmental linear systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2008

Vol. 56, nr 1

3-7

The concept of strong stability is extended for positive and compartmental linear systems. It is shown that: 1) the asymptotically stable positive and compartmental systems are strongly stable if the eigenvalues of the system matrix are distinct, 2) electrical circuits consisting of resistances, capacitances (inductances) and source voltages are strongly stable.

Singular Compartmental Linear Systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2003

Vol. 51, nr 4

409-419

Models of singular compartmental linear continuous-time and discrete-time systems are introduced. Solutions of the singular models in terms of the Drazin inverse of the models matrices are given. Necessary and sufficient conditions for the singular systems to be compartmental are established. A notion of P-equivalence is introduced and conditions for the P-equivalence of the compartmental and asymptotically stable positive system are derived.