Open Access Open Access  Restricted Access Subscription or Fee Access

LMI Approach for Robust Control of Interval System with Time Delay

(*) Corresponding author

Authors' affiliations



Robust control of uncertain time delay system is a challenging problem for control engineers. The problem becomes more difficult when the system is having interval parameters. This paper proposes a method for solving the problem of robust control of an uncertain time delay system with interval parameters. The interval system with time delay has been transformed to a nominal system with time delay. An LMI controller is designed for the nominal system corresponding to the interval system at different values of parametric uncertainties. Then among all the controllers of different cases of parametric uncertainties, determined the controllers which are suitable for all the cases. Then identified the common controllers which are also suitable for the interval system. From the singular value analysis and the worst case gain analysis, the best suitable controller for the nominal system has been determined. The method is illustrated using examples and is seen providing good control performance. The chosen controller is robust for the range of uncertainty associated with the system
Copyright © 2015 Praise Worthy Prize - All rights reserved.


LMI; Robust Control; Interval System; Time Delay

Full Text:



Richard, Jean-Pierre. "Time-delay systems: an overview of some recent advances and open problems." automatica 39.10 (2003): 1667-1694.

Albertos, Pedro, and Pedro García. "Robust control design for long time-delay systems." Journal of Process Control 19.10 (2009): 1640-1648.

Niculescu, Silviu-Iulian. Delay effects on stability: a robust control approach. Vol. 269. Springer Science & Business Media, 2001.

Jun, Myungsoo, and Michael G. Safonov. "IQC robustness analysis for time‐delay systems." International Journal of Robust and Nonlinear Control 11.15 (2001): 1455-1468.

Chen, Mou, and Wen-Hua Chen. "Disturbance-observer-based robust control for time delay uncertain systems." International Journal of Control, Automation and Systems 8.2 (2010): 445-453.

Kharitonov, V. L., and A. P. Zhabko. "Lyapunov–Krasovskii approach to the robust stability analysis of time-delay systems." Automatica 39.1 (2003): 15-20.

Yu, Li, and Jian Chu. "An LMI approach to guaranteed cost control of linear uncertain time-delay systems." Automatica 35.6 (1999): 1155-1159.

Hu, Sanqing, and Jun Wang. "On stabilization of a new class of linear time-invariant interval systems via constant state feedback control." IEEE Transactions on Automatic Control 45.11 (2000): 2106-2111.

Cai, Guangbin, Changhua Hu, and Guangren Duan. "Efficient LMI-based quadratic stability and stabilization of parameter-dependent interval systems with applications." International Journal of Innovative Computing, Information and Control 8 (2012): 1943-1954.

J.G.Lu and G.R.Chen “Robust stability and stabilization of fractional order interval systems: An LMI approach. IEEE Transactions on Automatic Control,vol.54,no.6 pp 1294-1299,2009.

Xiao, Min, Zhongke Shi, and Alexander I. Domoshnitsky. "Delay-Dependent Guaranteed Cost H Control of an Interval System with Interval Time-Varying Delay." Journal of Inequalities and Applications 2009 (2009): 26.

Mao, Weijie, and Xu Wang. "LMI conditions for quadratic and robust-stability of interval systems." Journal of Control Theory and Applications 4.2 (2006): 187-192.

Wang, Kaining, Anthony N. Michel, and Derong Liu. "Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices." Automatic Control, IEEE Transactions on 39.6 (1994): 1251-1255.

Kebriaei, Hamed, and A. Rahimi-Kian. "Robust Control of Interval Systems Using a Pole Placement Design." Control and Automation, 2007. ICCA 2007. IEEE International Conference on. IEEE, 2007.

Patre, B. M., and P. J. Deore. "Robust state feedback for interval systems: an interval analysis approach." Reliable Computing Journal 14 (2010): 46-60.

de Campos, Victor AF, José J. da Cruz, and Luiz C. Zanetta Jr. "Robust Control of Dynamical Systems Using Linear Matrix Inequalities and Norm-Bounded Uncertainty." Journal of Control, Automation and Electrical Systems 25.2 (2014): 151-160.

da Cruz Figueredo, Luis Felipe, et al. "Delay-Dependent Robust Stability Analysis for Time-Delay T–S Fuzzy Systems with Nonlinear Local Models."Journal of Control, Automation and Electrical Systems 24.1-2 (2013): 11-21.

El Ghaoui, Laurent, Eric Feron, and Venkataramanan Balakrishnan. Linear matrix inequalities in system and control theory. Vol. 15. Philadelphia: Society for industrial and applied mathematics, 1994.

Gahinet, P., Nemirovski, A., Laub, A. J., & Chilali, M. LMI Control Toolbox for use with Matlab. 1995. The MATH Works. Inc., Natick, MA.

D. Mary, "Motion Control of Tractor Trailer systems with multiple Active control via Hinfinity controller," Doctoral dissertation, India, 2014.

Khargonekar, Pramod P., Ian R. Petersen, and Kemin Zhou. "Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory." Automatic Control, IEEE Transactions on 35.3 (1990): 356-361.

GARCIA, GERMAIN, JACQUES BERNUSSOU, and DENIS ARZELIER. "Stabilization of an uncertain linear dynamic system by state and output feedback: a quadratic stabilizability approach." International journal of control64.5 (1996): 839-858.

Mary, A. Dolly. "Robust LMI based control of wheeled mobile robots." Computer Science & Education (ICCSE), 2011 6th International Conference on. IEEE, 2011.

D. Gorinevsky, S. Boyd, and G. Stein, Design of Low-Bandwidth Spatially Distributed Feedback, IEEE Transactions on Automatic Control, Vol. 53(Issue 1):257-272, February 2008.

Gudarzi, M., Oveisi, A., Ride Comfort Performance of Active Vehicle Suspension with Seat Actuator Based on Non-Fragile H∞ Controller, (2015) International Review on Modelling and Simulations (IREMOS), 8 (1), pp. 90-98.

Guisser, M., El-Jouni, A., Aboulfatah, M., Abdelmounim, E., Nonlinear MPPT controller for photovoltaic pumping system based on robust integral backstepping approach, (2014) International Review on Modelling and Simulations (IREMOS), 7 (3), pp. 481-488.

Grouz, F., Sbita, L., Robust adaptive backstepping control for wind energy systems with uncertain PMSGs, (2014) International Review on Modelling and Simulations (IREMOS), 7 (1), pp. 83-94.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize