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Robust stabilisation of discrete-time time-varying linear systems with Markovian switching and nonlinear parametric uncertainties

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  • Vasile Dragan

Abstract

In this paper, the problem of the robustness of the stability of a discrete-time linear stochastic system is addressed. The nominal plant is described by a discrete-time time-varying linear system subject to random jumping according with a non-homogeneous Markov chain with a finite number of states. The class of admissible uncertainties consists of multiplicative white noise type perturbations with unknown intensity. It is assumed that the intensity of white noise type perturbations is modelled by unknown nonlinear functions subject to linear growth conditions. The class of admissible controls consists of stabilising state feedback control laws. We show that the best robustness performance is achieved by the stability provided by a state feedback design based on the stabilising solution of a suitable discrete-time Riccati-type equation.

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  • Vasile Dragan, 2014. "Robust stabilisation of discrete-time time-varying linear systems with Markovian switching and nonlinear parametric uncertainties," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1508-1517, July.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:7:p:1508-1517
    DOI: 10.1080/00207721.2013.860643
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    References listed on IDEAS

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    1. Li Sheng & Ming Gao, 2013. "Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(2), pages 252-264.
    2. Xiao-Zheng Jin & Guang-Hong Yang & Xiao-Heng Chang, 2013. "Robust and adaptive tracking control against actuator faults with a linearised aircraft application," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 151-165.
    3. Gerardo Romero & Iván Díaz & Irma Pérez & Alfredo Guerrero & David Lara & José Rivera, 2013. "New results on robust stability for differential-difference systems with affine linear parametric uncertainty," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 14-22.
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