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)
Stability and implementable filters for singular systems with nonlinear perturbations. (English) Zbl 1176.93075
Summary: We investigate the problem of designing filter for a class of continuous-time uncertain singular systems with nonlinear perturbations, which can be realized in practice. The perturbation is a time-varying function of the system state and satisfies a Lipschitz constraint. The design objective is to guarantee that a prescribed upper bound on an performance of the robust filter is attained for all possible energy-bounded input disturbances and all admissible uncertainties and which can be implemented on-line to get a good replica of the state. We first establish sufficient condition for the existence and uniqueness of solution to the singular system connected with the normal filter. Using a linear matrix inequality (LMI) format, we then provide a sufficient condition for the asymptotic stability of the realizable filter. Then by means of a convex analysis procedure the filter gain matrices are derived and an important special case is readily deduced. Finally, a numerical example is presented to illustrate the theoretical developments.
MSC:
93E11Filtering in stochastic control
93B36H -control
References:
[1]Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice Hall, New York (1979)
[2]Aplevich, J.D.: Implicit Linear Systems. Springer, Berlin (1991)
[3]Bernstein, D.S., Haddad, W.M.: Steady-state Kalman filtering with an error bound. Syst. Control Lett. 16, 309–317 (1991) · Zbl 0729.93077 · doi:10.1016/0167-6911(91)90052-G
[4]Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
[5]Campbell, S.L.: Singular System of Differential Equations. Pitman, San Francisco (1982)
[6]Chen, S.J., Lin, J.L.: Robust stability of discrete time-delay uncertain singular systems. In: IEE Proceedings Control Theory and Applications, vol. 151, pp. 45–51 (2004)
[7]Dai, L.: Singular Control Systems. Springer, Berlin (1989)
[8]El Ghaoui, L., Oustry, F., Ait Rami, M.: A cone complementarity linearization algorithm for static output feedback control and related problems. IEEE Trans. Automat. Control. 42, 1171–1176 (1997) · Zbl 0887.93017 · doi:10.1109/9.618250
[9]Fu, M., de Souza, C.E., Xie, L.: H estimation for uncertain systems. Int. J. Robust Nonlinear Control 2, 87–105 (1992) · Zbl 0765.93032 · doi:10.1002/rnc.4590020202
[10]Gahinet, P., Apkarian, P.: A linear matrix inequality approach to control. Int. J. Robust Nonlinear Control 4, 421–448 (1994) · Zbl 0808.93024 · doi:10.1002/rnc.4590040403
[11]Geromel, J.C.: Optimal linear filtering with parameter uncertainty. IEEE Trans. Signal Process. 47, 168–175 (1999) · Zbl 0988.93082 · doi:10.1109/78.738249
[12]Ho, D.W.C., Lu, G.: Robust stabilization of a class of discrete-time nonlinear systems via output feedback: the unified LMI approach. Int. J. Control 76, 105–115 (2003) · Zbl 1026.93048 · doi:10.1080/0020717031000067367
[13]Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New York (2002)
[14]Lewis, F.L.: A survey of linear singular systems. Circuits Syst. Signal Process. 5, 3–36 (1986) · Zbl 0613.93029 · doi:10.1007/BF01600184
[15]Lin, C., Wang, J.L., Soh, C.B.: Robustness of uncertain descriptor systems. Syst. Control Lett. 31, 129–138 (1997) · Zbl 0901.93043 · doi:10.1016/S0167-6911(97)00038-8
[16]Lu, G., Ho, D.W.C.: Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation. IEEE Trans. Automat. Control 51, 818–823 (2006) · doi:10.1109/TAC.2006.875017
[17]Mahmoud, M.S., Al-Muthairi, N.F., Bingulac, S.: Robust Kalman filtering for continuous time-lag systems. Syst. Control Letters 38(4), 309–319 (1999) · Zbl 0986.93068 · doi:10.1016/S0167-6911(99)00068-7
[18]Mahmoud, M.S., Boujarwah, A.A.: Robust filtering for a class of linear parameter-varying systems. IEEE Trans. Circuits Syst. I 48(9), 1131–1138 (2001) · Zbl 1003.93050 · doi:10.1109/81.948442
[19]Mahmoud, M.S., Shi, P.: Robust Kalman filtering for continuous time-lag systems with jump parameters. IEEE Trans. Circuits Syst. I 50(1), 98–105 (2003) · doi:10.1109/TCSI.2002.807504
[20]Mahmoud, M.S.: Resilient linear filtering of uncertain systems. Automatica 40(10), 1797–1802 (2004) · Zbl 1162.93403 · doi:10.1016/j.automatica.2004.05.007
[21]Mahmoud, M.S.: Resilient Control of Uncertain Dynamical Systems. Springer, Berlin (2004)
[22]Mahmoud, M.S.: Resilient 2/filtering of polytopic systems with state-delays. In: Proceedings of IET Control Theory and Applications, vol. 1(1), pp. 141–150 (2007)
[23]Nagpal, K.M., Khargonekar, P.P.: Filtering and smoothing in setting. IEEE Trans. Automat. Control 36, 152–166 (1991) · Zbl 0758.93074 · doi:10.1109/9.67291
[24]Rehm, A., Allgower, F.: Self-scheduled output feedback control of descriptor systems. Comput. Chem. Eng. 24, 279–284 (2000) · doi:10.1016/S0098-1354(00)00478-6
[25]Xu, S., Dooren, P.V., Stefan, R., Lam, J.: Robust stability and stabilization for singular systems with state-delay and parameter uncertainty. IEEE Trans. Automat. Control. 47, 1122–1228 (2002) · doi:10.1109/TAC.2002.800651
[26]Xu, S., Lam, J., Zou, Y.: filtering for singular systems. IEEE Trans. Automat. Control. 48, 2217–2222 (2003) · doi:10.1109/TAC.2003.820138
[27]Xu, S., Lam, J.: Robust stability and stabilization of discrete singular systems: an equivalent characterization. IEEE Trans. Automat. Control. 49, 568–574 (2004) · doi:10.1109/TAC.2003.822854
[28]Yue, D., Han, Q.L.: Robust filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Trans. Signal Process. 52, 3200–3212 (2004) · doi:10.1109/TSP.2004.836535