## LPV systems with parameter-varying time delays: Analysis and control.(English)Zbl 0969.93020

The paper considers the system \begin{aligned} \dot x(t) &= A(\rho(t))x(t)+ A_h(\rho(t))x (t-h(\rho(t)))+ B(\rho(t)) u(t),\\ y(t) &= C(\rho(t))x(t)+ C_h(\rho(t)) x(t- h(\rho(t)))+ D(\rho(t)) u(t)\end{aligned} with bounded nonincreasing delay. Also $$\rho(\cdot)$$ is a function with bounded derivative. The authors develop a Lyapunov functional theory for linear stability of the equilibrium of the free system as well as for feedback stabilization.

### MSC:

 93C23 Control/observation systems governed by functional-differential equations 93D20 Asymptotic stability in control theory 93D15 Stabilization of systems by feedback

LMI toolbox
Full Text:

### References:

 [1] Apkarian, P.; Adams, R.J., Advanced gain-scheduling techniques for uncertain systems, IEEE transactions on control systems technology, 6, 21-32, (1998) [2] Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduled $$H∞$$ controllers, IEEE transactions on automatic control, 40, 853-864, (1995) · Zbl 0826.93028 [3] Becker, G.; Packard, A.K., Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback, Systems control letters, 23, 205-215, (1994) · Zbl 0815.93034 [4] Boyd, S.P.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004 [5] Dugard, L.; Verriest, E.I., Stability and control of time-delay systems, (1998), Springer London · Zbl 0901.00019 [6] Driver, R.D., Ordinary and delay differential equations, (1977), Springer New York · Zbl 0374.34001 [7] Gahinet, P.; Apkarian, P.; Chilali, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE transactions on automatic control, 41, 436-442, (1996) · Zbl 0854.93113 [8] Gahinet, P.; Nemirovskii, A.; Laub, A.J.; Chilali, M., LMI control toolbox, (1995), Mathworks Natick, MA [9] Skelton, R.E.; Iwasaki, T.; Grigoriadis, K.M., A unified algebraic approach to linear control design, (1998), Taylor & Francis London [10] Kolmanovskii, V.B.; Shaikhet, L.E., Control of systems with aftereffect, vol. 157, (1996), American Mathematical Society Providence, RI [11] Mahmoud, M.S.; Al-Muthairi, N.F., Design of robust controllers for time-delay systems, IEEE transactions on automatic control, 39, 995-999, (1994) · Zbl 0807.93049 [12] Malek-Zavarei, M.; Jamshidi, M., Time delay systems: analysis, optimization and applications, (1987), North-Holland Amsterdam · Zbl 0658.93001 [13] Packard, A.K., Gain scheduling via linear fractional transformations, Systems control letters, 22, 79-92, (1994) · Zbl 0792.93043 [14] Rugh, W.J., Analytical framework for gain scheduling, IEEE control systems magazine, 11, 74-84, (1991) [15] Scherer, C.W., Mixed H2/H∞ control for time-varying and linear parametrically varying systems, International journal of robust and nonlinear control, 6, 929-952, (1996) · Zbl 0861.93009 [16] Shamma, J.S.; Athans, M., Analysis of nonlinear gain-scheduled control systems, IEEE transactions on automatic control, 35, 898-907, (1990) · Zbl 0723.93022 [17] Shamma, J.S.; Athans, M., Gain scheduling: potential hazards and possible remedies, IEEE control systems magazine, 12, 101-107, (1992) [18] Vandenberghe, L.; Boyd, S., A primal-dual potential reduction method for problems involving matrix inequalities, Mathematical programming, 69, 205-236, (1994) · Zbl 0857.90104 [19] Verriest, E. (1994). Robust stability of time varying systems with unknown bounded delays. Proceedings of the 33rd IEEE Conference on decision and control, Orlando, FL (pp. 417-422). [20] Watanabe, K., Nobuyama, E., & Kojima, A. (1996). Recent advances in control of time delay systems: A tutorial review. Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan (pp. 2083-2089). [21] Wu, F.; Yang, X.H.; Packard, A.K.; Becker, G., Induced $$L2$$ norm control for LPV systems with bounded parameter variation rates, International journal of robust and nonlinear control, 6, 983-998, (1996) · Zbl 0863.93074
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.