# 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)
Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation. (English) Zbl 1194.93093
Summary: The problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

##### MSC:
 93C15 Control systems governed by ODE 93B52 Feedback control 93C73 Perturbations in control systems
Full Text:
##### References:
 [1] Bernstein, D. S.; Michel, A. N.: A chronological bibliography on saturating actuators, International journal of robust and nonlinear control 5, No. 5, 375-380 (1995) · Zbl 0841.93002 · doi:10.1002/rnc.4590050502 [2] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnam, V.: Linear matrix inequalities in systems and control theory, (1994) · Zbl 0816.93004 [3] Chen, H. G.; Han, K. W.: Improved quantitative measures of robustness for multivariable systems, IEEE transactions on automatic control 39, No. 4, 807-810 (1994) · Zbl 0807.93040 · doi:10.1109/9.286257 [4] Chen, J.; Patton, R. J.: Robust model-based fault diagnosis for dynamic systems, (1999) · Zbl 0920.93001 [5] Dai, L.: Singular control systems, (1989) · Zbl 0669.93034 [6] Fang, C. H.; Chang, F. R.: Analysis of stability robustness for generalized state-space systems with structured perturbations, Systems & control letters 21, No. 2, 109-114 (1993) · Zbl 0785.93072 · doi:10.1016/0167-6911(93)90113-K [7] Gahinet, P.; Apkarian, P.; Chilali, M.: Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE transactions on automatic control 41, No. 3, 436-442 (1996) · Zbl 0854.93113 · doi:10.1109/9.486646 [8] Gao, Z.; Brekin, T.; Wang, H.: Reliable observer-based control against sensor failures for systems with time delays in both state and input, IEEE transactions on systems, man and cybernetics--part A 38, No. 5, 1018-1029 (2008) [9] Gao, Z.; Ding, S.: State and disturbance estimator for time-delay systems with applications to fault estimation and signal compensation, IEEE transactions on signal processing 55, No. 12, 5541-5551 (2007) [10] Ho, D. W. C.; Lu, G.: Robust stabilization for a class of discrete-time nonlinear systems via output feedback: the unified LMI approach, International journal of control 76, No. 2, 105-115 (2003) · Zbl 1026.93048 · doi:10.1080/0020717031000067367 [11] Hu, T.; Lin, Z.: Control systems with actuator saturation: analysis and design, (2001) · Zbl 1061.93003 [12] Ioannou, P. A.; Sun, J.: Robust adaptive control, (1996) · Zbl 0839.93002 [13] Iwasaki, T.; Shibata, G.: LPV system analysis via quadratic separator for uncertain implicit systems, IEEE transactions on automatic control 46, No. 8, 1195-1208 (2001) · Zbl 1006.93053 · doi:10.1109/9.940924 [14] Lan, W.; Huang, J.: Semiglobal stabilization and output regulation of singular linear systems with input saturation, IEEE transactions on automatic control 48, No. 7, 1274-1280 (2003) [15] Lewis, F. L.: A survey of linear singular systems, Circuit systems and signal process 5, No. 1, 3-36 (1986) · Zbl 0613.93029 · doi:10.1007/BF01600184 [16] Liang, J. R.; Choi, H. L.; Lim, J. T.: On stability of singular systems with saturating actuators, IEICE tranctions on fundamentals of electronics communications and compute sciences 86A, No. 10, 2700-2703 (2003) [17] Lin, Z.: Low gain feedback, (1999) · Zbl 0927.93001 [18] Lin, Z.; Lv, L.: Set invariance conditions for singular systems subject to actuator saturation, IEEE transactions on automatic control 52, No. 12, 2351-2355 (2007) [19] Lin, Z.; Saberi, A.: Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks, Systems and control letters 24, No. 2, 125-132 (1995) · Zbl 0877.93095 · doi:10.1016/0167-6911(94)00020-V [20] Lu, G.; Ho, D. W. C.: Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation, IEEE transactions on automatic control 51, No. 5, 818-823 (2006) [21] Lv, L.; Lin, Z.: Analysis and design of singular linear systems under actuator saturation and L2/L$\infty$disturbances, Systems and control letters 57, No. 11, 904-912 (2008) · Zbl 1149.93030 · doi:10.1016/j.sysconle.2008.04.004 [22] Masubuchi, I.; Kamitane, Y.; Ohara, A.; Suda, N.: H$\infty$control for descriptor systems: A matrix inequalities approach, Automatica 33, No. 4, 669-673 (1997) · Zbl 0881.93024 · doi:10.1016/S0005-1098(96)00193-8 [23] Tarbouriech, S.; Gomes, Da Silva J.: Synthesis of controllers for continuous-time delay systems with saturating controls via lmi’s, IEEE transactions on automatic control 45, No. 1, 105-111 (2000) · Zbl 0978.93062 · doi:10.1109/9.827364 [24] Xia, Y.; Zhang, J.; Boukas, E. K.: Control for discrete singular hybrid systems, Automatica 44, No. 10, 2635-2641 (2008) · Zbl 1155.93359 · doi:10.1016/j.automatica.2008.02.027 [25] Xu, J.; Jia, Q.; Lee, T.: Adaptive robust control schemes for a class of nonlinear uncertain descriptor systems, IEEE transactions on circuits and systems--I 47, No. 6, 957-962 (2000) [26] Xu, S.; Lam, J.: Robust control and filtering of singular systems, (2006) · Zbl 1114.93005 [27] Xu, S.; Van Dooren, P.; Stefan, R.; Lam, J.: Robust stability and stabilization for singular systems with state delay and parameter uncertainty, IEEE transactions on automatic control 47, No. 7, 1122-1128 (2002) [28] Yang, G. H.; Ye, D.: Adaptive reliable H$\infty$filtering against sensor failures, IEEE transactions on signal processing 55, No. 7, 3161-3171 (2007) [29] Yan, W. Y.; Lam, J.: On quadratic stability of systems with structured uncertainty, IEEE transactions on automatic control 46, No. 11, 1799-1805 (2001) · Zbl 1034.93049 · doi:10.1109/9.964695 [30] Zhou, B.; Lam, J.; Duan, G. R.: An ARE approach to semi-global stabilization of discrete-time descriptor linear systems with input saturation, Systems and control letters 58, No. 8, 609-616 (2009) · Zbl 1166.93021 · doi:10.1016/j.sysconle.2009.03.009