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Original Articles

Singular perturbation margin and generalised gain margin for linear time-invariant systems

, &
Pages 11-29 | Received 01 Nov 2013, Accepted 16 Jun 2014, Published online: 24 Jul 2014

References

  • Bhattacharyya, S.P., Chapellat, H., & Keel, L.H. (1995). Robust control the parametric approach. Upper Saddle River, NJ: Prentice-Hall.
  • Bozorg, M., & Davison, E.J. (2006). Control of time delay processes with uncertain delays: Time delay stability margins. Journal of Process Control, 16(4), 403–408.
  • Cantoni, M., & Glover, K. (2000). Gap-metric robustness analysis of linear periodically time-varying feedback systems. SIAM Journal on Control and Optimization, 38(3), 803–822.
  • Cao, C., & Hovakimyan, N. (2007). Stability margins of L1 adaptive controller: Part II. In Proceedings of American Control Conference (pp. 3931–3936). New York, NY: Institute of Electrical and Electronics Engineers (IEEE).
  • Chang, C.H., & Chang, M.K. (1994). Analysis of gain margins and phase margins of a nonlinear reactor control system. IEEE Transactions on Nuclear Sciences, 41, 1686–1691.
  • Colonius, F., & Kliemann, W. (1996). The Lyapunov spectrum of families of time-varying matrices. Transactions of American Mathematical Society, 348(11), 4389–4408.
  • Dmitriev, M., & Kurina, G. (2006). Singular perturbations in control problems. Automation and Remote Control, 67(1), 1–43.
  • Ejea-Mart, J., Sanchis-Kilders, E., Maset, E., Ferreres, A., Blanes, J.M., Garrigos, A., ...Esteve, V. (2010). Phase margin degradation of a peak current controlled converter at reduced duty cycle. IEEE Transactions on Power Electronics, 25(4), 863–874.
  • El-Sakkary, A.K. (1985). The gap metric: Robustness of stabilization of feedback systems. IEEE Transactions on Automatic Control, 30(3), 240–247.
  • French, M. (2008). Adaptive control and robustness in the gap metric. IEEE Transactions on Automatic Control, 53(2), 461–478.
  • Han, K.W., & Thaler, G.J. (1966). Control system analysis and design using a parameter space method. IEEE Transactions on Automatic Control, 11, 560–563.
  • Hodel, S.A., Whorton, M., & Zhu, J.J. (2008). Stability metrics for simulation and flight-software assessment and monitoring of adaptive control assist compensators. In Proceedings of AIAA Guidance, Navigation and Control Conference (AIAA-2008-7005). Reston, VA: American Institute of Aeronautics and Astronautics (AIAA).
  • Hong, Y., & Yang, O.W.W. (2006). Design of an adaptive PI rate controller for streaming media traffic based on gain and phase margins. IEE Proceedings – Communications, 153(1), 5–14.
  • Kadalbajoo, M.K., & Patidar, K.C. (2003). Singularly perturbed problems in partial differential equations: A survey. Applied Mathematics and Computation, 134(2/3), 371–429.
  • Kamen, E.W. (1988). The poles and zeros of a linear time-varying system. Linear Algebra Applications, 98, 263–289.
  • Khalil, H.K. (2002). Nonlinear systems. Upper Saddle River, NJ: Prentice Hall.
  • Kokotovic, P.V., Khalil, H.K., & O’Reilly, J. (1986). Singular perturbations methods in control: Analysis and design. New York, NY: Academic Press.
  • Kokotovic, P.V., O’Malley Jr, R.E., & Sannuti, P. (1976). Singular perturbations and order reduction in control theory: An overview. Automatica, 12, 123–132.
  • Kuzmina, L.K. (2005). Some problems in stability theory of singularly perturbed systems with multiple time-scales. Nonlinear Analysis, 63, 1289–1297.
  • Nataraj, P.S.V., & Deshpande, M. (2004). An interval method to compute stability margins for fractional order systems. In A. Le Mehauté, J.A. Tenreiro Machado, J.C. Trigeassou, & J. Sabatier (Eds.), Proceedings of the First IFAC Workshop on Fractional Differentiation and Its Applications, FDA'04 (pp. 174–179), Bordeaux. Amsterdam: IFAC-Elsevier Ltd.
  • Panda, R.C. (2009). Model based PI tuning rule with ultimate gain and phase margin criteria. Instrumentation Science and Technology, 37, 557–573.
  • Saberi, A., & Khalil, H.K. (1984). Quadratic-type Lyapunov functions for singularly perturbed systems. IEEE Transactions on Automatic Control, 29(6), 542–550.
  • Siljak, D.D. (1964). Analysis and synthesis of feedback control systems in the parameter plane. IEEE Transactions on Industry Applications, IA-83, 466–473.
  • Siljak, D.D. (1969). Nonlinear systems – the parameter analysis and design. New York, NY: Wiley.
  • Vidyasagar, M. (1985). Control system synthesis. Cambridge, MA: MIT Press.
  • Weinmann, A. (2006). Stability margin and spherical uncertainty. Cybernetics and Systems, 37(7), 685–705.
  • Wilson, B.H., Eriylmaz, B., & Shafai, B. (1997). Improving control design for nonlinear parametric uncertainty. IEEE Transactions on Automatic Control, 66(6), 863–883.
  • Yang, X., & Zhu, J.J. (2010). A generalization of Chang transformation for linear time-varying systems. In Proceedings of IEEE Conference on Decision and Control (pp. 6863–6869). New York, NY: IEEE.
  • Yang, X., & Zhu, J.J. (2012a). Chang transformation for decoupling of singularly perturbed linear slowly time-varying systems. In Proceedings, IEEE Conference on Decision and Control (pp. 5755–5760). New York, NY: IEEE.
  • Yang, X., & Zhu, J.J. (2012b). Generalized gain margin for nonlinear systems. In Proceedings, American Control Conference (pp. 3316–3321). New York, NY: IEEE.
  • Yang, X., & Zhu, J.J. (2012c). Singular perturbation margin assessment of linear slowly time-varying systems. In Proceedings, IEEE Conference on Decision and Control (pp. 6547–6553). New York, NY: IEEE.
  • Yang, X., & Zhu, J.J. (2012d). Singular perturbation margin assessment of linear time-invariant systems via the Bauer-Fike theorems. In Proceedings, IEEE Conference on Decision and Control (pp. 6521–6528). New York, NY: IEEE.
  • Yang, X., & Zhu, J.J. (2012e). Singular perturbation margin for nonlinear time-invariant systems. In Proceedings, American Control Conference (pp. 3309–3315). New York, NY: IEEE.
  • Zames, G., & El-Sakkary, A.K. (1980). Unstable systems and feedback: The gap metric. In Proceedings of Allerton Conference (pp. 380–385). Champaign, IL: University of Illinois.
  • Zhu, J.J. (1993). A note on extension of the Eigenvalue concept. IEEE Control Systems Magazine, 13, 68–70.
  • Zhu, J.J. (1996). A necessary and sufficient stability criterion for linear time-varying systems. In Proceedings of 28th IEEE Southeastern Symposium on Systems Theory (pp. 115–119). New York, NY: IEEE.
  • Zhu, J.J., & Johnson, C.D. (1989). New results in the reduction of linear time-varying dynamical systems. Society for Industrial and Applied Mathematics, 27(3), 476–494.
  • Zhu, J.J., Liu, Y., & Hang, R. (2009). A spectral Lyapunov function for exponentially stable LTV systems. In Proceedings of American Control Conference (pp. 115–119). New York, NY: IEEE.
  • Zhu, J.J., Yang, X., & Hodel, A.S. (2010). A singular perturbation approach for time-domain assessment of phase margin. In Proceedings of American Control Conference (pp. 315–322). New York, NY: IEEE.

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