Linear discrete-time systems with Markovian jumps and mode dependent time-delay: Stability and stabilizability

This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI) techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

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

[2]  Mark W. Spong,et al.  ROBUST STABILIZATION FOR A CLASS OF NONLINEAR SYSTEMS. , 1986 .

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

[4]  M. Malek-Zavarei,et al.  Time-Delay Systems: Analysis, Optimization and Applications , 1987 .

[5]  K. Loparo,et al.  Stability and control of discrete-time jump linear systems , 1991 .

[6]  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..

[7]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[8]  El Kebir Boukas,et al.  Stability of discrete-time linear systems with Markovian jumping parameters , 1995, Math. Control. Signals Syst..

[9]  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..

[10]  El-Kébir Boukas,et al.  H/sub /spl infin// control for discrete-time linear systems with Markovian jumping parameters , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

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

[12]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

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

[14]  Xi Li,et al.  Delay-dependent robust H control of uncertain linear state-delayed systems , 1999, Autom..

[15]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[16]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[17]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .