Research Interests

 

• Time-delay Systems
• Robust Control
• Fault-tolerant Control

 

 

Stability of delay-differential systems of neutral type

 

This research considers the stability problem of linear delay-differential systems of neutral type that exist in practical systems such as the distributed networks containing lossless transmission lines, and population ecology. A discretized Lyapunov functional approach will be developed. The resulting stability criteria will be formulated in the form of a linear matrix inequality (LMI). For nominal systems, the analytical results will be approached with fine discretization. For uncertain systems, the new approach will be much less conservative. Numerical examples will show significant improvement over approaches in the literature.

 

Recent publications:

 

1.      Robust stability of uncertain delay-differential systems of neutral type. Automatica, 38, 719~723, 2002.

 

2.      On delay-dependent stability for neutral delay-differential systems. International Journal of Applied Mathematics and Computer Science, 2001, 11 (4), 965~976.

 

3.      A discretized Lyapunov functional approach to stability of linear delay-differential systems of neutral type (with X. Yu). In Proc. of the 15^th IFAC World Congress on Automatic Control, Barcelona, Spain, July 21-26, 2002.

 

 

On robust stability of uncertain time-delay systems

 

The robust stability of time-delay systems has been widely investigated in the last two decades. The practical examples of time-delay systems include engineering, communications and biological systems. The existence of delay in a practical system may induce instability, oscillation and poor performance. This research will consider the robust stability of uncertain time-delay systems. The uncertainty under consideration is a quadratic dissipative one that contains a norm-bounded uncertainty, a positive real uncertainty and an uncertainty satisfying the so-called integral quadratic constraints as special cases. Note that a norm-bounded uncertainty only considers the gain of the uncertainty regardless of its phase, where a positive real uncertainty only characterizes the phase allowing for an arbitrary gain. Clearly, the norm-bounded and positive real characterizations are conservative if information on both gain and the phase of the uncertainty is available. The project will develop a stability criterion based on discretized Laypunov functional method and will cover the some existing results in the literature as a special case.

 

Recent publications:

 

1.      New results for delay-dependent stability of linear systems with time-varying delay. International Journal of Systems Science, 2002, 33 (3), 213~228.

 

2.      Stability of linear systems with time-varying delay: A generalized discretized Lyapunov functional approach (with K. Gu). Asian Journal of Control, 2001, 3 (3), 170~180.

 

3.      On robust stability of time-delay systems with norm-bounded uncertainty (with K. Gu). IEEE Transactions on Automatic Control, 2001, AC-46 (9): 1426~1431.

 

4.      Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficient (with K. Gu, Albert C. J. Luo and S.-I. Niculescu). International Journal of Control, 2001, 74 (7): 737~744.

 

 

Robust H-inf synthesis and filtering of uncertain time-delay systems

 

This research is concerned with the problem of robust H-inf synthesis and filtering problem for linear uncertain time-delay systems. Based on Lyapunov functional approach, we will develop some methods for synthesizing robust H-inf state and dynamic output feedback control laws which guarantee the stability of the closed-loop system and reduces, to a prescribed level, the effect of disturbance input on the controlled output. Some sufficient criteria will be proposed in terms of linear matrix inequalities (LMIs). Examples will show the effectiveness of the approach.

 

Recent publications:

 

1.      Controller design for time-delay systems using discretized Lyapunov functional approach (with K. Gu). In Proc. of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December, 2000, pp. 2793~2798.

 

2.      Robust stabilization for uncertain time-varying delay constrained systems with delay-dependence (with D. Mehdi). International Journal of Applied Mathematics and Computer Science, 1999, 9 (2): 293~311.

 

3.      Robust H-inf controller synthesis for uncertain systems with multiple time-varying delays: An LMI approach (with D. Mehdi). In Proc. of the 14^th IFAC World Congress, Beijing, P. R. China, July 5-9, 1999, Vol. C, pp. 271~276.

 

 

Robust H-inf control of uncertain descriptor time-delay systems

 

This research will investigate the robust H-inf control problem of uncertain descriptor time-delay systems. Firstly, based on the decomposition-free method, robust stability criteria will be proposed. The regularity and nonimpulsiveness problems will be analysed simultaneously. Then we will also extend the discretized Laypunov functional method to this kind of system. A practical computational criterion will be given. The derived stability criteria are expressed in terms of a set of LMIs.

 

Based on a generalized Lyapunov function and matrix analysis technology, memoryless linear H-inf controller and H-2 controller design methods will be proposed. Mixed H-2/H-inf control will also be considered based on a solution of an optimisation problem including control of chaos.

 

 

Robust fault-tolerant control of uncertain time-delay systems

 

This research is concerned with robust fault-tolerant control for linear time-delay systems with actuator and/or sensor failures. The stability criteria will be formulated in the form of linear matrix inequalities (LMIs). The new design procedure will be proposed. Numerical examples will show the effectiveness of the approach.

 

Recent publications:

 

1.      A new feedback design method for uncertain continuous-time systems possessing integrity (with J.-S. Yu). Acta Automatica Sinica, 1998, 24 (6): 768~775; Also in Chinese Journal of Automation (an English translation from Acta Automatica Sinica, is published by Allerton Press, Inc., U.S.A.), 1999, 11 (2): 137~146.

 

2.      Design of controller possessing integrity for uncertain continuous-time systems (with J.-S. Yu and Z.-Z. Tang). In Proc of IEEE International Conference on Industrial Technology (IEEE '96 ICIT), Shanghai, P. R. China, Dec. 2-6, 1996, pp. 545~549 (The Proc is published by IEEE Service Center, The ISBN Code is 0-7803-3104-4).