In this paper, passive control and H∞ state feedback based on non-fragile observer are presented for a class of uncertain, nonlinear and input time-delay systems. Firstly, taking uncertainties, nonlinearities and input time-delay into account, non-fragile observer and controller are designed and the perturbations of controller gain and observer gain are processed. Secondly, for the dynamic disturbances, an appropriate non-fragile state feedback controller based on the observation is selected to prove that the states of closed-loop system can be passive and stabilized with H∞ performance for continuous time system. Moreover, the problems such as time-delay are handled in virtue of Lyapunov method and linear matrix inequalities (LMIs). Finally, the simulation results demonstrate the validity of the proposed control design method.
ChenH (2014) Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation. International Journal of Control, Automation and Systems12(6): 1216–1224.
2.
ChenHChenY (2016) Fractional-order generalized principle of self-support (FOGPSS) in control system design. Journal of Automatica Sinica4(3): 430–441. IEEE/CAA.
3.
ChenWMMaGWangLN, et al. (2018) Stabilization and H∞ control of neutral stochastic delay Markovian jump systems. International Journal of Systems Science49(1): 58–67.
4.
ChenLLiTChenY, et al. (2019) Robust passivity and feedback passification of a class of uncertain fractional-order linear systems. International Journal of Systems Science50(6): 1149–1162.
5.
ChenHLiHLYangYW, et al. (2020) Fixed-time output tracking control for extended nonholonomic chained-form systems with state observers. Measurement and Control53(3–4): 400–408.
6.
ChenHChenYWangMQ (2022) Trajectory tracking for underactuated surface vessels with time delays and unknown control directions. IET Control Theory and Applications50(1): 140–141.
7.
DadkhahNRodriguesL (2014) Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach. IET Control Theory and Applications8(8): 626–632.
8.
HoMTDattaABhattacharyyaSP (2001) Robust non-fragile PID controller design. International Journal of Robust Nonlinear Control Automatica11(4): 681–708.
9.
JiangBShiPMaoZ (2011) Sliding mode observer-based fault estimation for nonlinear networked control systems. Circuits, Systems, and Signal Processing30(1): 1–16.
10.
KrishnamurthyPKhorramiF (2014) Adaptive output feedback control of a general class of uncertain feedforward systems via a dynamic scaling approach. IET Control Theory and Applications5: 681–692.
11.
LiHJingXKarimiHR (2014) Output-feedback-based H∞ control for vehicle suspension systems with control delay. IEEE Transactions on Industrial Electronics61(1): 436–446.
12.
LiHLiuGFengG, et al. (2021) Leader-follower consensus of nonlinear time-delay multiagent systems: a time-varying gain approach. Automatica126: 109–444.
13.
LiuLHanZLiW (2010) H1 non-fragile observer-based sliding mode control for uncertain time-delay systems. Journal of the Franklin Institute347(4): 567–576.
14.
MaYGuNZhangG (2014) Non-fragile robust H∞ control for uncertain discrete-time singular systems with time-varying delays. Journal of the Franklin Institute351(6): 3163–3181.
15.
MathiyalaganKParkJHJungHY, et al. (2015) Non-fragile observer-based H∞ control for discrete-time systems using passivity theory. Circuits Systems Signal Process34(7): 2499–2516.
16.
MohamedO (2022) Continuous stabilization of composite stochastic systems. IFAC-PapersOnLine55(12): 713–716.
17.
MuhammadSCerezoAD (2012) Passivity-based control applied to the dynamic positioning of ships. IET Control Theory & Applications6(5): 680–688.
18.
ParkJH (2004) Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections. International Journal of Systems Science35(4): 233–241.
19.
PengYZYuXJTingCX, et al. (2022) Means and the Schur complement of sector matrices. Linear and Multilinear Algebra70(13): 2611–2617.
20.
RenJZhangG (2012) Non-fragile PD state H1 control for a class of uncertain descriptor systems. Applied Mathematics and Computation218: 8806–8815.
21.
ShaoYLiuXSunX, et al. (2018) A delay decomposition approach to H∞ admissibility for discrete time singular delay systems. Information Science279: 893–905.
22.
ShenHXuSSongX, et al. (2012) Passivity-based control for Markovian jump systems via retarded output feedback. Circuits, Systems, and Signal Processing31(1): 189–202.
23.
SouzaSELiX (1999) Delay-dependent robust H∞ control of uncertain linear state-delayed systems. Automatica35(7): 1313–1321.
24.
SouzaAEfimovDRaïssiT, et al. (2022) Robust output feedback model predictive control for constrained linear systems via interval observers. Automatica135: 109–151.
25.
SuXWuLShiP, et al. (2014) A novel approach to output feedback control of fuzzy stochastic systems. Automatica50(12): 3269–3275.
26.
WangJShenH (2014) Parameter estimation of fuzzy neural network controller based on a modified differential evolution. Neurocomputing143: 51–56.
27.
WuLZhengW (2009) Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica45(9): 2120–2127.
28.
XieL (1996) Output feedback H∞ control of systems with parameter uncertainty. International Journal of Control63: 741–750.
29.
YueDLamJ (2005) Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays. Optimal Control Applications & Methods26: 85–105.
30.
ZhangYShiPNguangSK, et al. (2022) Observer-based finite-time fuzzy H∞ control for discretetime systems with stochastic jumps and time-delays. Signal Processing97(1): 252–261.
