zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Optimal guaranteed cost control of linear systems with mixed interval time-varying delayed state and control. (English) Zbl 1237.49047
Summary: This paper deals with the problem of optimal guaranteed cost control for linear systems with interval time-varying delayed state and control. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. A linear-quadratic cost function is considered as a performance measure for the closed-loop system. By constructing a set of augmented Lyapunov-Krasovskii functional combined with Newton-Leibniz formula, a guaranteed cost controller design is presented and sufficient conditions for the existence of a guaranteed cost state-feedback for the system are given in terms of Linear Matrix Inequalities (LMIs). Numerical examples illustrate the effectiveness of the obtained result.
MSC:
49N10Linear-quadratic optimal control problems
49K40Sensitivity, stability, well-posedness of optimal solutions
34H05ODE in connection with control problems
49M30Other numerical methods in calculus of variations
References:
[1]Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, New York (1993)
[2]Kolmanovskii, V., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic, Dordrecht (1992)
[3]Udwadia, F.: Noncollocated control of distributed-parameter nondispersive systems with tip Inertias using time Delays. Appl. Math. Comput. 47(1), 47–75 (1992) · Zbl 0745.93024 · doi:10.1016/0096-3003(92)90064-8
[4]Udwadia, F.E., Kumar, R.: Time-delayed control of classically damped structural systems. Int. J. Control 60(5), 687–713 (1994) · Zbl 0825.93255 · doi:10.1080/00207179408921490
[5]Udwadia, F.E., Hosseini, M., Chen, Y.: Robust control of uncertain systems with time-varying delays in control input. In: Proc. of the American Control Conference, USA, pp. 3840–3845 (1997)
[6]Udwadia, F.E., von Bremen, H., Kumar, R., Hosseini, M.: Time delayed control of structural systems. Earthquake Eng. Struct. Dyn. 32(2), 495–535 (2003) · doi:10.1002/eqe.228
[7]Udwadia, F.E., Phohomsiri, P.: Active control of structures Using time delayed positive feedback proportional control designs. Struct. Control Health Monit. 13(1), 536–552 (2006) · doi:10.1002/stc.128
[8]Udwadia, F.E., Hubertus von, B, Phohomsiri, P.: Time-delayed control design for active control of structures: principles and applications. Struct. Control Health Monit. 14(1), 27–61 (2007) · doi:10.1002/stc.82
[9]Fu, D., Bai, Y., Sun, M.: Delay-dependent H dynamic output feedback control for systems with time-varying delay. In: IEEE International Conference on Control and Automation Christchurch, New Zealand, IEEE, New York (2009)
[10]Chang, S.S.L., Peng, T.K.C.: Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Trans. Autom. Control 17(3), 474–483 (1972) · Zbl 0259.93018 · doi:10.1109/TAC.1972.1100037
[11]Petersen, I.R., Macfarlane, D.C.: Optimal guaranteed cost control and filtering uncertain linear systems. IEEE Trans. Autom. Control 39(10), 1971–1977 (1994) · Zbl 0817.93025 · doi:10.1109/9.317138
[12]Fischman, A., Dion, J.M., Dugard, L., Neto, A.T.: A linear matrix inequality approach for guaranteed cost control. In: Proc. 13th IFAC World Congress, San Fransisco, USA, vol. 4, pp. 197–202 (1996)
[13]Yu, L., Chu, J.: An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica 35(6), 1155–1159 (1999) · Zbl 1041.93530 · doi:10.1016/S0005-1098(99)00007-2
[14]Li, H., Niculescu, S.L., Dugard, L., Dion, J.M.: Robust guaranteed cost control of uncertain linear time-delay systems using dynamic output feedback. Math. Comput. Simul. 45, 349–358 (1998) · doi:10.1016/S0378-4754(97)00114-6
[15]Costa, E.F., Oliveira, V.A.: On the design of guaranteed cost controllers for a class of uncertain linear systems. Syst. Control Lett. 46(1), 17–29 (2002) · Zbl 0994.93013 · doi:10.1016/S0167-6911(01)00198-0
[16]Park, J.H.: Delay-dependent criterion for guaranteed cost control of neutral delay systems. J. Optim. Theory Appl. 124(3), 491–502 (2005) · Zbl 1070.93039 · doi:10.1007/s10957-004-0947-8
[17]Shi, P., Boukas, E.K., Shi, Y., Kagarwal, R: Optimal guaranteed cost control of uncertain discrete time-delay systems. J. Comput. Appl. Math. 157(3), 435–451 (2003) · Zbl 1029.93044 · doi:10.1016/S0377-0427(03)00433-3
[18]Chen, W.H., Guan, Z.H., Lu, X.: Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delay. J. Franklin Inst. 341, 419–430 (2004) · Zbl 1055.93054 · doi:10.1016/j.jfranklin.2004.04.003
[19]Zuo, Z.Q., Wang, Y.J.: Novel optimal guaranteed cost control of uncertain discrete systems with both state and input delays. J. Optim. Theory Appl. 139(1), 159–170 (2008) · Zbl 1152.93029 · doi:10.1007/s10957-008-9411-5
[20]Yang, D., Cai, K.Y.: Reliable guaranteed cost sampling control for nonlinear time-delay systems. Math. Comput. Simul. 80(10), 2005–2018 (2010) · Zbl 1196.93048 · doi:10.1016/j.matcom.2010.03.004
[21]Yang, J., Luo, W., Li, G., Zhong, S.: Reliable guaranteed cost control for uncertain fuzzy neutral systems. Nonlinear Anal. Hybrid Syst 4(2), 644–658 (2010) · Zbl 1203.93114 · doi:10.1016/j.nahs.2010.04.003
[22]Kwon, O.M., Park, J.H., Lee, S.M.: Exponential stability for uncertain dynamic systems with time-varying delays: LMI optimization approach. J. Optim. Theory Appl. 137(3), 521–532 (2008) · Zbl 1146.93030 · doi:10.1007/s10957-008-9357-7
[23]Hien, L.V., Phat, V.N.: Exponential stability and stabilization of a class of uncertain linear time-delay systems. J. Franklin Inst. 346, 611–625 (2009) · Zbl 1169.93396 · doi:10.1016/j.jfranklin.2009.03.001
[24]Nam, P.T., Phat, V.N.: Robust stabilization of linear systems with delayed state and control. J. Optim. Theory Appl. 140(2), 287–299 (2009) · Zbl 1159.93027 · doi:10.1007/s10957-008-9453-8
[25]Phat, V.N, Ha, Q.P., Trinh, H.: Parameter-dependent H control for time-varying delay polytopic systems. J. Optim. Theory Appl. 147(1), 58–70 (2010) · Zbl 1205.93134 · doi:10.1007/s10957-010-9707-0
[26]Shao, H.: New delay-dependent stability criteria for systems with interval delay. Automatica 45(3), 744–749 (2009) · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010
[27]Yoneyama, J.: Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling. Appl. Soft Comput. 11(2), 249–255 (2011) · doi:10.1016/j.asoc.2009.11.015
[28]Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003)
[29]Boyd, S., Ghaoui, El., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities and Control Theory. SIAM Studies in Applied Mathematic, vol. 15, SIAM, Philadelphia (1994)
[30]Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M.: LMI Control Toolbox for Use with MATLAB. The MathWorks, Natick (1995)