This paper uses the linear matrix inequality dilation approach to deal with robust stability and H∞ dynamic output feedback controller synthesis for linear parameter varying delayed systems with variable delay. This approach can express the original non-convex problem in terms of convex linear matrix inequalities and consequently reduces the conservatism of linear matrix inequality synthesis without dilation. Both delay-dependent stability and H∞ performance are studied in a quadratic context. Furthermore, a Lyapunov–Krasovskii functional is used to derive a delay-dependent criterion formulated in terms of a linear matrix inequality that will be used to search for an H∞ linear parameter varying delayed dynamic output feedback controller. To achieve this aim we use an integral inequality which plays a key role in the derivation of this criterion and enables the reduction of the H∞ cost in comparison to other results.
ApkarianPBiannicJMGahinetP (1995) Self scheduled H∞ control of missile via linear matrix inequalities. Journal of Guidance, Control and Dynamics18(3): 532–538.
2.
ApkarianPTuanHDBernussouJ (2001) Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations. IEEE Transactions on Automatic Control46(12): 1941–1946.
3.
BeibeiXDiyiCHaoZet al. (2015) Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit. Nonlinear Dynamics81(3): 1263–1274.
4.
BeibeiXDiyiCHaoZet al. (2017) Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag. Communications in Nonlinear Science and Numerical simulation47: 35–47.
5.
BriatCSenameOLafayJ (2009) Delay-scheduled state-feedback design for time-delay systems with time-varying delays: A LPV approach. Systems and Control Letters58(9): 664–671.
6.
BriatCSenameOLafayJ (2013) Memory resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays. Systems and Control Letters59(8): 451–459.
7.
ChengWYiS (2014) Delay-dependent robust H∞ control for uncertain stochastic systems with time-varying delays in state and control input. Journal of Systems and Control Engineering228(8): 565–577.
8.
ChilaliMGahinetP (1996) H∞ design with pole placement constraints: An LMI approach. IEEE Transactions on Automatic Control41(3): 327–354.
9.
ChoiHDAhnCKLimMTet al. (2016) A dynamic output-feedback H∞ control for active half-vehicle suspension systems with time-varying input delay. International Journal of Control, Automation and Systems14(1): 59–68.
10.
DaafouzJBernussouJGeromelJC (2008) On inexact LPV control design of continuous-time polytopic systems. IEEE Transaction on Automatic Control53(7): 1674–1678.
11.
EbiharaYHagiwaraT (2004) New dilated LMI characterizations for continuous-time multiobjective controller synthesis. Automatica40(11): 2003–2009.
12.
EbiharaYHagiwaraT (2005) A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems. Automatica41(11): 1933–1941.
13.
GahinetPApkarianP (1994) A linear matrix inequality approach to H∞ controls. International Journal of Robust and Non Linear Control4(4): 421–448.
14.
HeYWuMSheJHet al. (2004) Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Transactions On Automatic Control49(5): 828–832.
15.
HongminLXinyongW (2016) Adaptive tracking control for a class of uncertain switched nonlinear systems with time-delay. Transactions of the Institute of Measurement and Control74(14): 1447–1455.
16.
KaoCRantzerA (2007) Stability analysis of systems with uncertain time-varying delays. Automatica43(6): 959–970.
17.
LiHJingXKarimiHR (2014) Output-feedback based H∞ control for vehicle suspension systems with control delay. IEEE Transactions on Industrial Electronics61(1): 436–446.
18.
OliveiraRPeresP (2005) Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions. Linear Algebra and its Applications405(28): 209–228.
19.
OnatCKucukdemiralIBSivriogluSet al. (2009) LPV gain-scheduling controller design for a non-linear quarter-vehicle active suspension system. Transactions of the Institute of Measurement and Control31(1): 71–95.
20.
ParkPGLeeWILeeSY (2015) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. Journal of the Franklin Institute352(4): 1378–1396.
21.
RughWJShammaJS (2000) Research on gain scheduling. Automatica36(10): 1401–1425.
22.
SchererCGahinetPChilaliM (1997) Multiobjective output-feedback control via LMI optimization. IEEE Transactions on Automatic Control42(7): 896–911.
23.
SeronMMDe DonáJA (2015) Robust fault estimation and compensation for LPV systems under actuator and sensor faults. Automatica52: 294–301.
24.
ShammaJAthansM (1991) Guaranteed properties of gains scheduled control for linear parameter-varying plants. Automatica27(3): 559–564.
25.
SuplinVFridmanEShakedU (2006) H∞ control of linear uncertain time-delay systems: A projection approach. IEEE Transactions on Automatic Control51(3): 680–685.
26.
TuanHApkarianPNguyenT (2001) Robust and reduced order filtering: New LMI-based characterizations and methods. IEEE Transactions on Signal Processing49(12): 2875–2984.
27.
TuanHApkarianPNguyenT (2003) Robust filtering for uncertain non linearly parametrized plants. EEE Transactions on Signal Processing51(7): 1806–1815.
28.
WuF (2001) A generalized LPV system analysis and control synthesis framework. International Journal of Control74(7): 745–759.
29.
WuFGrigoriadisKM (2001) LPV systems with parameter-varying time delays: Analysis and control. Automatica37(2): 221–229 .
30.
XieW (2008) New LMI-based condition for quadratic stabilization of LPV system. Journal of Inequalities and Application2008: 563845, 12 p.
31.
XieWEisakaT (2004) Design of LPV control systems based on Youla parameterization. IET Control Theory & Applications151(4): 465–472 .
32.
XiaYJiaY (2003) Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals. Systems and Control Letters50(3): 183–193.
33.
YingboHJingNXingWet al. (2016) Robust adaptive control for vehicle active suspension systems with uncertain dynamics. Transactions of the Institute of Measurement and Control31(9): 1251–1261.
34.
ZhangFGrigoriadisK (2005) Delay-dependent stability analysis and H∞ control for state-delayed LPV system. In: Mediterranean conference on control and automation, Limassol, Cyprus, 27–29 June 2005, pp.1532–1537. IEEE.
35.
ZhangXTsiotrasPKnospeC (2002) Stability analysis of LPV time-delayed systems. International Journal of Control75(7): 538–558.
36.
ZhangXMWuMSheJHet al. (2005) Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica41(8): 1405–1412.
37.
ZhangYYangFHanQL (2014) H∞ control of LPV systems with randomly multi-step sensor delays. International Journal of Control, Automation, and Systems12(6): 1207–1215.
38.
ZhongQ (2006) Robust Control of Time-Delay Systems. London: Springer–Verlag.
