Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method
The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. New criteria for exponential stability are derived usi...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/7417909 |
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| _version_ | 1832550022929973248 |
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| author | Josef Diblík |
| author_facet | Josef Diblík |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed. |
| format | Article |
| id | doaj-art-a4ee8c2d636f4dbcadda28ec4b195c9b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a4ee8c2d636f4dbcadda28ec4b195c9b2025-02-03T06:08:04ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/74179097417909Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second MethodJosef Diblík0Central European Institute of Technology (CEITEC), Brno University of Technology, Brno, Czech RepublicThe paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+∑i=1sBikxk-mik, k=0,1,… , where s∈N, A is a constant square matrix, Bik are square matrices, mik∈N∪0, and mik≤m for an m∈N. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.http://dx.doi.org/10.1155/2017/7417909 |
| spellingShingle | Josef Diblík Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method Discrete Dynamics in Nature and Society |
| title | Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method |
| title_full | Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method |
| title_fullStr | Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method |
| title_full_unstemmed | Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method |
| title_short | Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method |
| title_sort | exponential stability of linear discrete systems with variable delays via lyapunov second method |
| url | http://dx.doi.org/10.1155/2017/7417909 |
| work_keys_str_mv | AT josefdiblik exponentialstabilityoflineardiscretesystemswithvariabledelaysvialyapunovsecondmethod |