A POLYNOMIAL METHOD FOR STABILITY ANALYSIS OF LTI SYSTEMS INDEPENDENT OF DELAYS


ALIKOC B., Ergenç A. F.

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, cilt.55, ss.2661-2683, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 55 Konu: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1137/16m1077726
  • Dergi Adı: SIAM JOURNAL ON CONTROL AND OPTIMIZATION
  • Sayfa Sayıları: ss.2661-2683

Özet

A new method providing necessary and sufficient conditions to test delay-independent stability for general linear time-invariant systems with constant delays is proposed. The method is utilized for single delay and incommensurate multiple delay systems. The proposed method offers an approach to determine the exact boundaries of unknown parameters such as controller gains or system parameters ensuring delay-independent stability, in addition to exhibiting an efficient test for real parameters. The technique is based on nonexistence of unitary complex zeros of an auxiliary characteristic polynomial obtained via extended Kronecker summation. A special feature of the polynomial, i.e., the self-inversive property, is proved and utilized to check its unitary zeros to determine delay-independent stability by an efficient zero location test. The methodology is executed employing simple algebraic operations and inspection of the number of sign variations in the obtained sequence. For the single delay case, the procedure does not require parameter (or frequency) sweeping, equation solving, and pointwise testing even for the determination of the delay-independent stabilizing regions of unknown parameters. In the case of systems with p multiple delays, (p - 2) agent parameters in the range [0, 2 pi] and one agent parameter in the range [0, pi] are swept to determine delay-independent stability without the requirement of solving equations. A graphical projection approach for multiple delays is proposed in the case in which unknown parameters exist. The complete delay-independent stability analysis of a second order PD-controlled system with single delay is presented. Moreover, the method is applied to find the exact delay-independent stabilizing regions of unknown parameters of systems with two and three delays.