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Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems

Author

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  • Jun Zhou
  • Ketian Gao
  • Xinbiao Lu

Abstract

Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

Suggested Citation

  • Jun Zhou & Ketian Gao & Xinbiao Lu, 2018. "Complex Scaling Approach for Stability Analysis and Stabilization of Multiple Time-Delayed Systems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-14, April.
    • Handle: RePEc:hin:jnlmpe:8492735
    DOI: 10.1155/2018/8492735
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