Delay-dependent robust stability conditions and decay estimates for systems with input delays. (English) Zbl 1274.93217

Summary: The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test robust stability criteria. The problem of constrained control is also discussed, and alternative stability tests for the case of saturation nonlinearities are presented. Estimates of the transient behavior of the controlled system are also obtained. Finally, an example illustrates the results.


93D09 Robust stability
93D21 Adaptive or robust stabilization
93C41 Control/observation systems with incomplete information
Full Text: Link


[1] Bernstein D., Michel A. N.: A chronological bibliography on saturated actuators. Internat. J. Robust and Nonlinear Control 5 (1995), 375-380 · Zbl 0841.93002
[2] Bourlès H.: \(\alpha \)-stability of systems governed by functional differential equations - extensions of results for linear delay systems. Internat. J. Control 45 (1987), 2233-2238 · Zbl 0637.93058
[3] Bourlès H., Kosmidou O. I.: On the quadratic stability of uncertain systems in the presence of time-delays. Proceedings of the European Control Conference ECC’97, Brussels 1997
[4] Chen B. S., Wang S., Lu H. C.: Stabilization of time-delay systems containing saturating actuators. Internat. J. Control 47 (1988), 867-881 · Zbl 0636.93063
[5] Choi H. H., Chung M. J.: Memoryless \(H_{\infty }\) controller design for linear systems with delayed state and control. Automatica 31 (1995), 917-919 · Zbl 0829.93021
[6] Halanay A.: Differential Equations. Academic Press, New York 1966 · Zbl 0912.34002
[7] Hale J. K., Lunel S. M. V.: Introduction to Functional Differential Equations. Springer-Verlag, New York 1993 · Zbl 0787.34002
[8] Hrissagis K., Crisalle O.: Robust stabilization of input constrained bilinear systems. Proceedings of the IFAC’96 World Congress, San Francisco 1996
[9] Hrissagis K., Crisalle O.: Simple robust stability tests for time-delay systems with nonlinearities: Application to CSTR with recycle. Workshop on Industrial Control Systems, Thessaloniki 1996
[10] Inamdar S. R., Kumar V. R., Kulkarni B. D.: Dynamics of reacting systems in the presence of time-delay. Chem. Engrg. Sci. 46 (1991), 901-908
[11] Kolmanovskii V. B., Nosov V. R.: Theory of Functional Differential Equations. Academic Press, New York 1985
[12] Krikelis N. J., Barkas S. K.: Design of tracking systems subject to actuator saturation and integrator wind-up. Internat. J. Control 39 (1984), 667-682 · Zbl 0532.93023
[13] Kwon W. H., Pearson A. E.: Feedback stabilization of linear systems with delayed control. IEEE Trans. Automat. Control 25 (1980), 266-269 · Zbl 0438.93055
[14] Lee J. H., Lee Y. I., Kwon W. H.: \(H_{\infty }\) controllers for input delayed systems. Proceedings of Conf. on Decision and Control, Lake Buena vista 1994
[15] Mori T. N.: Criteria for asymptotic stability of linear time-delay systems. IEEE Trans. Automat. Control 30 (1985), 158-161 · Zbl 0557.93058
[16] Schell M., Ross J.: Effects of time-delay in rate processes. J. Chem. Phys. 85 (1986), 6489-6503
[17] Shen J.-C., Kung F.-C.: Stabilization of input delay systems with saturating actuator. Internat. J. Control 50 (1989), 1667-1680 · Zbl 0687.93063
[18] Vidyasagar M.: Nonlinear Systems Analysis. Second edition. Prentice Hall, Englewood Cliffs, N. J. 1993 · Zbl 1006.93001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.