This paper deals with the stabilization of state-constrained linear parameter-varying systems subject to parameter uncertainties and input saturation. Based on a class of parameter-dependent Lyapunov functions, and the set invariance, sufficient conditions for the stabilization problem of the linear parameter-varying systems are established in terms of parameterized linear matrix inequalities. Further, these conditions are converted into linear matrix inequalities by using a parameter relaxation technique. Finally, detailed simulation results are presented to illustrate the effectiveness of the proposed methodology.
CaoYYLinZShamashY (2002) Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation. Systems & Control Letters46(2): 137–151.
2.
DoALSilvaJMJrSenameOet al. (2011) Control design for LPV systems with input saturation and state constraints: An application to a semi-active suspension. In: Proceedings of the 50th IEEE conference on decision and control and European control conference, pp. 3416–3421.
3.
FangHJLinZLHuQL (2004) Analysis of linear systems in the presence of actuator saturation and L2 disturbances. Automatica40(7): 1229–1238.
4.
GahinetPApkarianP (1994) A linear matrix inequality approach to H∞ control. International Journal of Robust and Nonlinear Control4(4): 421–448.
5.
GahinetPApkarianPChilaliM (1996) Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Transactions on Automatic Control41(3): 436–442.
6.
GilbertWHenrionDBernussouJet al. (2010) Polynomial LPV synthesis applied to turbofan engines. Control Engineering Practice18(9): 1077–1083.
7.
GlattfelderAHSchaufelbergerW (2003) Control Systems with Input and Output Constraints. London: Springer Science & Business Media.
8.
HeXZhaoJ (2012) Parameter-dependent H∞ filter design for LPV systems and an autopilot application. Applied Mathematics and Computation218(9): 5508–5517.
9.
HuTLinZ (2001) Control Systems with Actuator Saturation: Analysis and Design. London: Springer Science & Business Media.
10.
HuTTeelARZaccarianL (2008) Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance. Automatica44(2): 512–519.
11.
JinX (2016) Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems. International Journal of Robust and Nonlinear Control26(2): 286–302.
12.
KogisoKHirataK (2009) Reference governor for constrained systems with time-varying references. Robotics and Autonomous Systems57(3): 289–295.
13.
LiYLiTJingX (2014) Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function. International Journal of Adaptive Control and Signal Processing28(2): 184–199.
14.
LiYLinZ (2014) Saturation-based switching anti-windup design for linear systems with nested input saturation. Automatica50(11): 2888–2896.
15.
MohammadpourJSchererCW (2012) Control of Linear Parameter Varying Systems with Applications. Boston: Springer Science & Business Media.
16.
NiuBZhaoJ (2013a) Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function. International Journal of Systems Science44(5): 978–985.
17.
NiuBZhaoJ (2013b) Brief paper-output tracking control for a class of switched non-linear systems with partial state constraints. IEE Proceedings - Control Theory and Applications7(4): 623–631.
18.
ParkBYYunSWParkPG (2012) H2 state-feedback control for LPV systems with input saturation and matched disturbance. Nonlinear Dynamics67(2): 1083–1096.
19.
ParkJHKimTHSugieT (2011) Output feedback model predictive control for LPV systems based on quasi-min–max algorithm. Automatica47(9): 2052–2058.
20.
ParkPGChoiDJ (2001) LPV controller design for the nonlinear RTAC system. International Journal of Robust and Nonlinear Control11(14): 1343–1363.
21.
PrimeZCazzolatoBDoolanCet al. (2010) Linear-parameter-varying control of an improved three-degree-of-freedom aeroelastic model. Journal of Guidance, Control and Dynamics33(2): 615–619.
22.
RimonEKoditschekDE (1992) Exact robot navigation using artificial potential functions. IEEE Transactions on Robotics and Automation8(5): 501–518.
23.
RöthigAAdamyJ (2016) On stabilizing linear systems with input saturation via soft variable structure control laws. Systems & Control Letters89: 47–54.
24.
SkeltonREIwasakiTGrigoriadisKM (1998) A Unified Algebraic Approach to Linear Control Design. London: Taylor & Francis.
25.
TabatabaeipourSMStoustrupJBakT (2015) Fault-tolerant control of discrete-time LPV systems using virtual actuators and sensors. International Journal of Robust and Nonlinear Control25(5): 707–734.
26.
WieBBernsteinDS (1992) Benchmark problems for robust control design. Journal of Guidance, Control and Dynamics15(5): 1057–1059.
27.
WitteJBaliniHSchererCW (2010) Robust and LPV control of an AMB system. In: Proceedings of American Control Conference (ACC), Baltimore, Maryland, USA, July 2010, pp. 2194–s2199.
28.
WuFGrigoriadisKM (2001) LPV systems with parameter-varying time delays: Analysis and control. Automatica37(2): 221–229.
29.
WuFGrigoriadisKMPackardA (1998) Anti-windup controller synthesis via linear parameter-varying control design methods. In: Proceedings of the 1998 American Control Conference, Philadelphia, PA, USA, June 1998, pp. 343–347.
30.
WuLYangXLiF (2013) Nonfragile output tracking control of hypersonic air-breathing vehicles with an LPV model. IEEE/ASME Transactions on Mechatronics18(4): 1280–1288.
31.
XieW (2005) H2 gain scheduled state feedback for LPV system with new LMI formulation. IEE Proceedings - Control Theory and Applications152(6): 693–697.
32.
XieW (2012) Multi-objective performance controller synthesis for LPV systems. Asian Journal of Control14(5): 1273–1281.
33.
YanPÖzbayH (2007) On switching controllers for a class of linear parameter varying systems. Systems & Control Letters56(7): 504–511.
34.
YunSWChoiYJParkPG (2010) State-feedback disturbance attenuation for polytopic LPV systems with input saturation. International Journal of Robust and Nonlinear Control20(8): 899–922.
35.
ZhouBGaoHLinZet al. (2012) Stabilization of linear systems with distributed input delay and input saturation. Automatica48(5): 712–724.
36.
ZhouBLinZDuanG (2010) Robust global stabilization of linear systems with input saturation via gain scheduling. International Journal of Robust and Nonlinear Control20(4): 424–447.
37.
ZuoZWangY (2007) An improved set invariance analysis and gain-scheduled control of LPV systems subject to actuator saturation. Circuits, Systems & Signal Processing26(5): 635–649.
