Abstract
The problem of \({H_\infty }\) robust exponential stability and static output feedback stabilization of uncertain singular time-delay systems with saturating actuators are investigated. First, the delay-dependent condition is given to guarantee that the singular time-delay systems are not only exponential admissible, but also satisfies \(H_{\infty }\) performance \(\gamma \). Moreover, the estimation of stability region and the design method of \(H_{\infty }\) static output feedback controller are given by solving a convex optimization problem. Some simulation examples are provided to demonstrate the merit of the proposed design methods.
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References
Cao YY, Lin ZL, Hu TS (2002) Stability analysis of linear time-delay systems subjected to input saturation. IEEE Trans Circ Syst I Fundam Theory Appl 49:233–240
Dai L (1989) Singular control systems, Lecture notes in control and information sciences
Dey R, Rakshit A, Ray G, Ghosh S (2012) New delay-dependent stabilization result for linear time-delay system with actuator saturation, power, signals, controls and computation (EPSCICON). In: 2012 International Conference, pp 1–6
Feng J, Lam J, Li P, Shu Z (2011) Decay rate constrained stabilization of positive systems using static output feedback. Int J Robust Nonlinear Control 21:44–54
Fridman E, Pila A, Shaked U (2003) Regional stabilization and \({H_\infty }\) control of time-delay systems with saturating actuators. Int J Robust Nonlinear Control 13:885–907
Fridman E, Shaked U (2002) \({H_\infty }\) control of linear state-delay descriptor systems: an LMI approach. Linear Algebra Appl 351–352(1):271–302
Haidar A, Boukas EK, Xu S, Lam J (2009) Exponential stability and static output feedback stabilisation of singular time-delay systems with saturating actuators. IET Control Theory Appl 3(9):1293–1305
Hu TS, Lin ZL, Chen BM (2002) Analysis and design for discrete-time linear systems subject to actuator saturation. Syst Control Lett 45:97–112
Lan WY, Huang J (2003) Semiglobal stabilization and output regulation of singular linear systems with input saturation. IEEE Trans Autom Control 48:1274–1280
Li Y, Tong S, Li T (2015) Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control direction and unknown dead-zones. IEEE Trans Fuzzy Syst 23(4):1228–1241
Li Y, Tong S, Li T (2016) Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation. IEEE Trans Fuzzy Syst 24(4):41–853
Long F, Li CL, Cui CZ (2010) Dynamic output feedback \({H_\infty }\) control for a class of switched linear systems with exponential uncertainty. Int J Innov Comput Inf Control 6:1727–1736
Lu RQ, Yang PJ, Bai JJ, Xue AK (2016) Quantized observer-based sliding mode control for networked control system via the time-delay approach. Circ Syst Signal Process 35:1563–1577
Ma SP, Zhang CG (2011) \({H_\infty }\) control for discrete-time singular markov jump systems subject to actuator saturation. J Frankl Inst 349(3):1011–1029
Ma YC, Fu L, Jing YH, Zhang QL (2015) Finite-time \({H_\infty }\) control for a class of discrete-time switched singular time-delay systems subject to actuator saturation. Appl Math Comput 261:264–283
Pachpatte BG (1973) A note on Gronwall–Bellman iequality. J Math Anal Appl 44:758–762
Shu Z, Lam J (2008) Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays. Int J Control 81:865–882
Singh V (2004) Robust stability of cell neural networks with delay: linear matrix inequality approach. IEE Proc Control Theory Apply 151:125–129
Tian JK, Zhong SM, Wang Y (2012) Improved exponential stability criteria for neural networks with time-delays. Neurocomputing 97:164–173
Tyan F, Bernstein DS (1997) Dynamic output feedback compensation for linear systems with independent amplitude and rate saturations. Int J Control 67:89–116
Wu ZG, Su HY, Chu J (2010) Delay-dependent robust exponential stability of uncertain singular systems with time delays. Int J Innov Comput Inf Control 6:2275–2283
Wu ZG, Zhou W (2007) Delay-dependent robust control for uncertain singular time-delay systems. IET Control Theory Appl 1:1234–1241
Yang F, Zhang QL (2005) Delay-dependent \({H_\infty }\) control for linear descriptor systems with delay instate. J Control Theory Appl 3:76–84
Zhai D, An L, Li J, Zhang Q (2016) Fault detection for stochastic parameter-varying markovian jump systems with application to networked control systems. Appl Math Model 40(3):2368–2383
Zhai D, Xi C, An L, Dong J (2016) Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time. IEEE Trans Syst Man Cybern Syst, pp 1–13. doi:10.1109/TSMC.2016.2571338
Zhong R, Yang Z (2006) Delay-dependent robust control of descriptor systems with time delay. Asian J Control 8:36–44
Acknowledgements
This work was supported by the National Natural Science Foundation of ChinaNo. 61273004, and the Natural Science Foundation of Hebei province No. F2014203085. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.
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Communicated by Antonio José Silva Neto.
This work is supported by National Natural Science Foundation of China (No. 61273004) and the Natural Science Foundation of Hebei province (No. F2014203085).
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Ma, Y., Fu, L. Robust \({H_\infty }\) control for singular time-delay systems with saturating actuators via static output feedback. Comp. Appl. Math. 37, 2260–2276 (2018). https://doi.org/10.1007/s40314-017-0450-0
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DOI: https://doi.org/10.1007/s40314-017-0450-0