About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays
<p/> <p>This paper discusses nonnegativity and positivity concepts and related properties for the state and output trajectory solutions of dynamic linear time-invariant systems described by functional differential equations subject to point time delays. The various nonnegativities and po...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
|
| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2007/025872 |
| _version_ | 1811283680480460800 |
|---|---|
| author | De la Sen M |
| author_facet | De la Sen M |
| author_sort | De la Sen M |
| collection | DOAJ |
| description | <p/> <p>This paper discusses nonnegativity and positivity concepts and related properties for the state and output trajectory solutions of dynamic linear time-invariant systems described by functional differential equations subject to point time delays. The various nonnegativities and positivities are introduced hierarchically from the weakest one to the strongest one while separating the corresponding properties when applied to the state space or to the output space as well as for the zero-initial state or zero-input responses. The formulation is first developed by defining cones for the input, state and output spaces of the dynamic system, and then extended, in particular, to cones being the three first orthants each being of the corresponding dimension of the input, state, and output spaces.</p> |
| first_indexed | 2024-04-13T02:15:59Z |
| format | Article |
| id | doaj.art-79322d1c3cb145309c216395f23be5f7 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-13T02:15:59Z |
| publishDate | 2007-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-79322d1c3cb145309c216395f23be5f72022-12-22T03:07:08ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2007-01-0120071025872About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point DelaysDe la Sen M<p/> <p>This paper discusses nonnegativity and positivity concepts and related properties for the state and output trajectory solutions of dynamic linear time-invariant systems described by functional differential equations subject to point time delays. The various nonnegativities and positivities are introduced hierarchically from the weakest one to the strongest one while separating the corresponding properties when applied to the state space or to the output space as well as for the zero-initial state or zero-input responses. The formulation is first developed by defining cones for the input, state and output spaces of the dynamic system, and then extended, in particular, to cones being the three first orthants each being of the corresponding dimension of the input, state, and output spaces.</p>http://www.journalofinequalitiesandapplications.com/content/2007/025872 |
| spellingShingle | De la Sen M About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays Journal of Inequalities and Applications |
| title | About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays |
| title_full | About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays |
| title_fullStr | About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays |
| title_full_unstemmed | About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays |
| title_short | About <inline-formula><graphic file="1029-242X-2007-025872-i1.gif"/></inline-formula>-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays |
| title_sort | about inline formula graphic file 1029 242x 2007 025872 i1 gif inline formula positivity properties of time invariant linear systems subject to point delays |
| url | http://www.journalofinequalitiesandapplications.com/content/2007/025872 |
| work_keys_str_mv | AT delasenm aboutinlineformulagraphicfile1029242x2007025872i1gifinlineformulapositivitypropertiesoftimeinvariantlinearsystemssubjecttopointdelays |