Abstract
This chapter addresses the problem of state feedback guaranteed cost control for uncertain GRNs with interval time-varying delays. The involved norm-bounded uncertainties are first transformed into external disturbances, and then an LKF approach combined with the convex technique and cone complementarity linearization technique is proposed to investigate a sufficient condition for the existence of expected controllers. Thereby, we design a state feedback guaranteed cost controller which guarantees the resultant closed-loop system is robustly asymptotically stable and its linear quadratic performance has an upper bound. A numerical example is provided to show the effectiveness of the proposed method.
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References
Chang, S., Peng, T.: Adaptive guaranteed cost control of systems with uncertain parameters. IEEE Trans. Autom. Control 17(4), 474–483 (1972)
Chen, L.L., Zhou, Y., Zhang, X.: Guaranteed cost control for uncertain genetic regulatory networks with interval time-varying delays. Neurocomputing 131, 105–112 (2014)
Ghaoui, L.E., Oustry, F., AitRami, M.: A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control 42(8), 1171–1176 (1997)
He, Y., Wu, M., Liu, G.P., She, J.H.: Output feedback stabilization for a discrete-time system with a time-varying delay. IEEE Trans. Autom. Control 53(10), 2372–2377 (2008)
He, Y., Zeng, J., Wu, M., Zhang, C.K.: Robust stabilization and \(H_{\infty }\) controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties. Math. Biosci. 236(1), 53–63 (2012)
Hu, J.Q., Liang, J.L., Cao, J.D.: Stabilization of genetic regulatory networks with mixed time-delays: an adaptive control approach. IMA J. Math. Control Inf. 32(2), 343–358 (2015)
Li, L., Yang, Y.Q.: On sampled-data control for stabilization of genetic regulatory networks with leakage delays. Neurocomputing 149, 1225–1231 (2015)
Liu, A.D., Yu, L., Zhang, D., Zhang, W.A.: Finite-time \({H_\infty }\) control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities. J. Franklin Inst. 350(7), 1944–1961 (2013)
Liu, Z., Jiang, H.: Exponential stability of genetic regulatory networks with mixed delays by periodically intermittent control. Neural Comput. Appl. 21(6), 1263–1269 (2012)
Lu, L., Xing, Z., He, B.: Non-uniform sampled-data control for stochastic passivity and passification of Markov jump genetic regulatory networks with time-varying delays. Neurocomputing 171, 434–443 (2016)
Mathiyalagan, K., Sakthivel, R.: Robust stabilization and \(H_{\infty }\) control for discrete-time stochastic genetic regulatory networks with time delays. Can. J. Phys. 90(10), 939–953 (2012)
Moradi, H., Majd, V.J.: Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: a redesign approach. Math. Biosci. 275, 10–17 (2016)
Pan, W., Wang, Z., Gao, H., Li, Y., Du, M.: Robust \(H_{\infty }\) feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise. Int. J. Robust Nonlinear Control 20(18), 2093–2107 (2010)
Shao, H.: New delay-dependent stability criteria for systems with interval delay. Automatica 45(3), 744–749 (2009)
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Zhang, X., Wang, Y., Wu, L. (2019). Guaranteed Cost Control for Delayed GRNs. In: Analysis and Design of Delayed Genetic Regulatory Networks. Studies in Systems, Decision and Control, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-030-17098-1_8
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DOI: https://doi.org/10.1007/978-3-030-17098-1_8
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