Guaranteed cost control of uncertain discrete-time systems with delay in state

This paper considers the problems of robust guaranteed cost control of linear discrete timedelay systems with parametric uncertainties. By linear matrix inequality (LMI) approach, the robust quadratic stability of the system is studied. A control design method is developed such that the closed-loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays. Furthermore, the upper bound (cost) can be optimized by incorporating with a minimization problem.

[1]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[2]  Il Hong Suh,et al.  On stabilization by local state feedback for discrete-time large-scale systems with delays in interconnections , 1982 .

[3]  S. Gutman,et al.  Properties of Min-Max Controllers in Uncertain Dynamical Systems , 1982 .

[4]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[5]  R. Mukundan,et al.  Memoryless feedback control in uncertain dynamic delay systems , 1986 .

[6]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[7]  J. Doyle,et al.  Quadratic stability with real and complex perturbations , 1990 .

[8]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[9]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .

[10]  Lihua Xie,et al.  On designing controllers for a class of uncertain sampled-data nonlinear systems , 1993 .

[11]  Sérgio Ricardo de Souza,et al.  ℋ2 guaranteed cost control for uncertain discrete-time linear systems , 1993 .

[12]  P. Peres,et al.  H ∞ guaranteed cost control for uncertain continuous-time linear systems , 1993 .

[13]  W. Kwon,et al.  Memoryless H∞ controllers for state delayed systems , 1994, IEEE Trans. Autom. Control..

[14]  Naser F. Al-Muthairi,et al.  Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties , 1994, IEEE Trans. Autom. Control..

[15]  Sing Kiong Nguang,et al.  Robust stabilisation for a class of time-delay nonlinear systems , 1994 .

[16]  Jong Hae Kim,et al.  Robust control for parameter uncertain delay systems in state and control input , 1996, Autom..

[17]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[18]  E. Boukas,et al.  Robust Stabilizability of Uncertain Linear Time-Delay Systems With Markovian Jumping Parameters , 1996 .

[19]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[20]  El-Kébir Boukas,et al.  Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters , 1997 .

[21]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[22]  Ian R. Petersen,et al.  Optimal guaranteed cost control of discrete‐time uncertain linear systems , 1998 .

[23]  Seong-Ho Song,et al.  H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state , 1998, Autom..

[24]  Peng Shi,et al.  Robust control for Markovian jumping discrete-time systems , 1999, Int. J. Syst. Sci..