Diagonally-Invariant Exponential Stability
| Authors: | Pastravanu Octavian, Technical University “Gh. Asachi” of Iasi, Romania
Mihaela-Hanako Matcovschi, Technical University “Gh. Asachi” of Iasi, Romania
Mihail Voicu, Technical University “Gh. Asachi” of Iasi, Romania |
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| Topic: | 2.2 Linear Control Systems |
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| Session: | Linear Systems III |
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| Keywords: | stability analysis, invariant sets, continuous-time systems, matrix measures, comparison methods |
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Abstract
The diagonally-invariant exponential stability (DIES) is introduced as a special type of exponential stability (ES) which incorporates information about the sets invariant with respect to the state-space trajectories. DIES is able to unify, at the conceptual level, issues in stability analysis that have been separately addressed by previous researches Unlike ES, DIES is a norm-dependent property and its study requires appropriate instruments. These instruments are derived in terms of matrix measures from the characteristics of the system trajectories; their convenient exploitation in practice is ensured by methods based on matrix comparisons. The developed framework presents a noticeable generality and its applicability is illustrated for several classes of linear and non-linear systems. This framework can be simply adapted to discrete-time systems.
