OPTIMAL D-STABLE CONTROL FOR DISCRETE MULTIPLE TIME-DELAY SYSTEMS WITH PARAMETRIC UNCERTAINTIES

Abstract The robustly optimal D -stable problem is considered in this study for discrete multiple time-delay systems with parametric uncertainties. A discrete uncertain multiple time-delay system can be transformed into another system with no delay by properly defining new state variables. The problem of optimization of discrete-time systems with multiple time delays is consequently reduced to a standard discrete linear quadratic regulator problem A robust criterion of D -stability is derived on the basis of D -pole placement technique to show that the optimal control law not only minimizes the discrete linear quadratic performance index but also simultaneously guarantees that all poles of the closed-loop system remain inside the specified disk D ( α , r ) in the presence of parametric uncertainties. An example is finally provided for illustrating our main results.

[1]  Sang Bong Kim,et al.  Pole assignment in a specified disk , 1987 .

[2]  T. Mori,et al.  Delay-independent stability criteria for discrete-delay systems , 1982 .

[3]  J. Farison,et al.  Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems , 1989 .

[4]  Tsu-Tien Lee,et al.  Discrete optimal control with eigenvalue assigned inside a circular region , 1986 .

[5]  M. Ikeda,et al.  Stabilization of linear systems with time-varying delay , 1979 .

[6]  Engin Yaz,et al.  Stability robustness of linear discrete-time systems in the presence of uncertainty , 1989 .

[7]  Tzuu-Hseng S. Li,et al.  D-stability analysis for discrete systems with a time delay , 1992 .

[8]  Yau-Tarng Juang,et al.  Lyapunov approach to robust pole-assignment analysis , 1989 .

[9]  T. Mori,et al.  Simple stability criteria for single and composite linear systems with time delays , 1981 .

[10]  A. Rachid.  Robustness of pole assignment in a specified region for perturbed systems , 1990 .

[11]  N. Patel,et al.  Optimal control of systems described by delay differential equations , 1982 .

[12]  T. Mori.  Criteria for asymptotic stability of linear time-delay systems , 1985, IEEE Transactions on Automatic Control.

[13]  Bor-Sen Chen,et al.  Robust stability of uncertain time-delay systems , 1987 .

[14]  Bor-Sen Chen,et al.  Dynamical Feedback Compensator for Uncertain Time-Delay Systems Containing Saturating Actuator , 1989 .

[15]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[16]  Abdul-Amir A. Abdul-Wahab.  Lyapunov bounds for root clustering in the presence of system uncertainty , 1990 .

[17]  Tsu-Tian Lee,et al.  Optimal pole assignment for a discrete linear regulator with constant disturbances , 1987 .

[18]  A. Feliachi,et al.  Memoryless stabilization of linear delay-differential systems , 1981 .

[19]  Antonio Vicino.  Robustness of pole location in perturbed systems , 1989, Autom..

[20]  E. Lee,et al.  Sampled data hereditary systems: Linear quadratic theory , 1986 .

[21]  Tsu-Tian Lee,et al.  Discrete-time optimal control for linear time-delay systems with deterministic disturbances , 1991 .

[22]  Feng-Hsiag Hsiao,et al.  Determination of the Tolerable Sector of Series Nonlinearities in Uncertain Time-Delay Systems Under Dynamical Output Feedback , 1991 .