On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays
The property of external positivity of dynamic systems is commonly defined as the non-negativity of the output for all time under zero initial conditions and any given non-negative input for all time. This paper investigates the extension of that property for a structured class of initial conditions...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Systems |
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| Online Access: | https://www.mdpi.com/2079-8954/10/1/9 |
| _version_ | 1797476353566572544 |
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| author | Manuel De la Sen |
| author_facet | Manuel De la Sen |
| author_sort | Manuel De la Sen |
| collection | DOAJ |
| description | The property of external positivity of dynamic systems is commonly defined as the non-negativity of the output for all time under zero initial conditions and any given non-negative input for all time. This paper investigates the extension of that property for a structured class of initial conditions of a single-input single-output (SISO) linear dynamic system which can include, in general, certain negative initial conditions. The above class of initial conditions is characterized analytically based on the structure of the transfer function. The basic study is performed in the delay-free case, but extensions are then given for systems subject to a finite number of internal and external, in general incommensurate, point delays and for the closed-loop dynamic systems which incorporate a feedback compensator. The formulation relies on calculating the output based on the impulse responses by considering the relation of the mentioned sets of structured initial conditions with the zero-state response which allows to keep the non-negativity of the zero-input response and that of the total response provided the non-negativity for all time of the zero-state response. |
| first_indexed | 2024-03-09T20:57:42Z |
| format | Article |
| id | doaj.art-aac16989e6194dc1b41cf1a567ac1af7 |
| institution | Directory Open Access Journal |
| issn | 2079-8954 |
| language | English |
| last_indexed | 2024-03-09T20:57:42Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Systems |
| spelling | doaj.art-aac16989e6194dc1b41cf1a567ac1af72023-11-23T22:18:31ZengMDPI AGSystems2079-89542022-01-01101910.3390/systems10010009On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External DelaysManuel De la Sen0Institute of Research and Development of Processes IIDP, Department of Electricity and Electronics, Faculty of Science and Technology, Campus of Leioa, University of the Basque Country, 48940 Leioa, SpainThe property of external positivity of dynamic systems is commonly defined as the non-negativity of the output for all time under zero initial conditions and any given non-negative input for all time. This paper investigates the extension of that property for a structured class of initial conditions of a single-input single-output (SISO) linear dynamic system which can include, in general, certain negative initial conditions. The above class of initial conditions is characterized analytically based on the structure of the transfer function. The basic study is performed in the delay-free case, but extensions are then given for systems subject to a finite number of internal and external, in general incommensurate, point delays and for the closed-loop dynamic systems which incorporate a feedback compensator. The formulation relies on calculating the output based on the impulse responses by considering the relation of the mentioned sets of structured initial conditions with the zero-state response which allows to keep the non-negativity of the zero-input response and that of the total response provided the non-negativity for all time of the zero-state response.https://www.mdpi.com/2079-8954/10/1/9internal and external positivityinternal delaysexternal delays |
| spellingShingle | Manuel De la Sen On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays Systems internal and external positivity internal delays external delays |
| title | On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays |
| title_full | On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays |
| title_fullStr | On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays |
| title_full_unstemmed | On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays |
| title_short | On the External Positivity of SISO Linear Dynamic Systems under a Class of Nonzero and Possibly Negative Initial Conditions Eventually Subject to Incommensurate Point Internal and External Delays |
| title_sort | on the external positivity of siso linear dynamic systems under a class of nonzero and possibly negative initial conditions eventually subject to incommensurate point internal and external delays |
| topic | internal and external positivity internal delays external delays |
| url | https://www.mdpi.com/2079-8954/10/1/9 |
| work_keys_str_mv | AT manueldelasen ontheexternalpositivityofsisolineardynamicsystemsunderaclassofnonzeroandpossiblynegativeinitialconditionseventuallysubjecttoincommensuratepointinternalandexternaldelays |