Research ArticleOpen AccessGoogle Scholar indexed
New Stability Tests of Positive Standard and Fractional Linear Systems
- 1
Circuits and Systems·Volume 02 (2011)·Pages 261–268·Published 17 October 2011·DOI10.4236/cs.2011.24036
Copy link · social · email
Abstract
New tests for checking asymptotic stability of positive 1D continuous-time and discrete-time linear systems without and with delays and of positive 2D linear systems described by the general and the Roesser models are proposed. Checking of the asymptotic stability of positive 2D linear systems is reduced to checking of suitable corresponding 1D positive linear systems. It is shown that the stability tests can be also applied to checking the asymptotic stability of fractional discrete-time linear systems with delays. Effectiveness of the tests is shown on numerical examples.
KeywordsFractionalPositiveLinearSystemAsymptotic StabilityTest
- L. Farina and S. Rinaldi, “Positive Linear Systems; Theory and Applications,” John Wiley & Sons, Hoboken, 2000. doi:10.1002/9781118033029
- T. Kaczorek, “Positive 1D and 2D Systems,” Springer Verlag, London, 2002. doi:10.1007/978-1-4471-0221-2
- M. Bus?owicz, “Simple Stability Conditions for Linear Systems with Delays,” Bulletin of the Polish Academy of Sciences, Vol. 56, No. 4, 2008, 319-324.
- M. Bus?owicz, “Robust Stability of Positive Discrete-Time Linear Systems of Fractional Order,” Bulletin of the Polish Academy of Sciences, Vol. 58, No. 4, 2010, 567-572. doi:10.2478/v10175-010-0057-8
- T. Kaczorek, “Stability of Positive Continuous-Time Linear Systems with Delays,” Bulletin of the Polish Academy of Sciences, Vol. 57, No. 4, 2009, 395-398. doi:10.2478/v10175-010-0143-y
- T. Kaczorek, “Independence of Asymptotic Stability of Positive 2D Linear Systems with Delays of Their Delays,” International Journal of Applied Mathematics and Computer Science, Vol. 19, No. 2, 2009, 255-261. doi:10.2478/v10006-009-0021-7
- T. Kaczorek, “Asymptotic Stability of Positive 2D Linear Systems with Delays,” Bulletin of the Polish Academy of Sciences, Vol. 57, No. 2, 2009, 133-138. doi:10.2478/v10175-010-0113-4
- T. Kaczorek, “Asymptotic Stability of Positive 2D Linear Systems,” Computer Applications in Electrical Engineering, Poznan University of Technology, Electrical Engineering Committee of Polish Academy of Sciences, IEEE Poland Section, Poznan.
- T. Kaczorek, “Stability and Stabilization of Positive Fractional Linear Systems by State-Feedbacks,” Bulletin of the Polish Academy of Sciences, Vol. 58, No. 4, 2010, 517-554.
- T. Kaczorek, “Selected Problems of Fractional System Theory,” Springer Verlag, London, 2011. doi:10.1007/978-3-642-20502-6
- K. S. Narendra and R. Shorten, “Hurwitz Stability of Metzler Matrices,” IEEE Transactions on Automatic Control, Vol. 55, no. 6 June 2010, pp. 1484-1487. doi:10.1109/TAC.2010.2045694
- T. Kaczorek, “New Stability Tests of Positive 1D and 2D Linear Systems,” Proceeding of 25th European Conference Modelling and Simulation, Krakow, 7-10 June 2011.