A new technique is presented for the design of gain-scheduling controllers for switched systems with actuator saturation. By using the parametric Lyapunov equation-based approach and the invariant set theory, we develop a switching strategy of the whole system and propose a gain scheduling approach to increase the design parameter online. Then the closed-loop system is proven to be exponentially stable. Numerical simulations show the effectiveness of the proposed gain scheduling approaches.
AframAJanabi-SharifiF (2014) Theory and applications of HVAC control systems: a review of model predictive control (MPC). Building and Environment72: 343–355.
2.
BenzaouiaABenhayounMMesquineF (2014) Stabilization of systems with unsymmetrical saturated control: an LMI approach. Circuits, Systems, and Signal Processing33: 3263–3275.
3.
ChenHWangCLZhangBW. (2012) Saturated tracking control for nonholonomic mobile robots with dynamic feedback. Transactions of the Institute of Measurement and Control35: 105–116.
4.
GuoRW (2011) Stability analysis and control design of multiple-equilibrium switched systems. PhD Dissertation, Shandong University, China.
LauKMiddletonRH (2003) Switched integrator control schemes for integrating plants. European Journal of Control9: 539–559.
7.
LiDXiY (2010) The feedback robust MPC for LPV systems with bounded rates of parameter changes. IEEE Transactions on Automatic Control55: 503–507.
8.
LiDXiYZhengP (2009) Constrained robust feedback model predictive control for uncertain systems with polytopic description. International Journal of Control82: 1267–1274.
9.
LiDWXiYGLinZL (2011) An Nth-step set invariance approach to the analysis and design of discrete-time linear systems subject to actuator saturation. Systems & Control Letters60: 943–951
10.
LiLLJunZGeorgiMD (2013) Multiple Lyapunov functions approach to observer based H-inf control for switched systems. International Journal of System Science44: 812–819.
11.
LiberzonD (2003) Switching in Systems and Control. Boston: Birkhauser.
12.
LiberzonDMorseS (1999) Basic problems in stability and design of switched systems. Control Systems Magazine19: 59–70.
13.
LiberzonDTempoR (2004) Common Lyapunov functions and gradient algorithms. IEEE Transactions on Automatic Control49: 990–994.
14.
LinHAntsaklisPJ (2009) Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Transactions on Automatic Control54: 308–322.
15.
LinZL (1998) Low Gain Feedback. London: Springer.
16.
LinZLSaberiA (1993) Semi-global exponential stabilization of linear systems subject to ‘input saturation’ via linear feedbacks. Systems & Control Letters21: 225–239.
17.
LinZLSaberiA (1995) Semi-global exponential stabilization of linear discrete-time systems subject to ‘input saturation’ via linear feedbacks. Systems & Control Letters24: 125–132.
18.
LuoJMZhaoJ (2014) A generalized multiple Lyapunov functions method based non-fragile guaranteed cost control for uncertain switched fuzzy systems. Applied Mathematics and Computation237: 494–500.
19.
MazencFde QueirozMSMalisoffM. (2006) Further results on active magnetic bearing control with input saturation. IEEE Transactions on Control System Technology14: 914–919.
20.
NiWChengDZ (2010) Control of switched linear systems with input saturation. International Journal of Systems Science41: 1057–1065.
21.
ShortenRCorlessMMiddletonR. (2009) A quadratic stability result for singular switched with application to anti-windup control. In Proceedings of American Control Conference, St. Louis, MO, USA, 10–12 June, pp. 1917–1922.
22.
SunZGeSS (2005) Switched Linear Systems: Control and Design. London: Springer.
23.
TeelAR (1995) Semi-global stabilization of null linear controllable systems with input nonlinearities. IEEE Transactions on Automatic Control40: 96–100.
24.
TingCSLiuCS (2011) Stabilization of nonlinear time-delay systems with input saturation via anti-windup fuzzy design. Soft Computing15: 877–888.
25.
WangLPZhuJParkJH (2012) A probabilistic approach for model following of Markovian jump linear systems subject to actuator saturation. International Journal of Control, Automation, and Systems10: 1042–1048.
26.
WangQZhouBDuanGR (2013) Discrete gain scheduled control of the input saturation systems with applications in on-orbit rendezvous. Acta Automatica Sinica40: 1698–1704.
27.
WuXJLinZL (2014) Dynamic anti-windup design for anticipatory activation: enlargement of the domain of attraction. Science China Information Sciences57: 1–14.
28.
XiangWMXiaoJ (2012) Stability analysis and control synthesis of switched impulsive systems. International Journal Robust Nonlinear Control22:1440–1459.
29.
XiangZRXiangWM (2009) Stability analysis of switched systems under dynamical dwell time control approach. International Journal of Systems Science40: 347–355.
30.
XieXXuHLZhangR (2014) Exponential stabilization of impulsive switched systems with time delays using guaranteed cost control. In Abstract and Applied Analysis. Hindawi Publishing Corporation.
31.
XuHLLiuXZTeoKL (2008) A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays. Nonlinear Analysis: Hybrid Systems2: 38–50.
32.
YangCDZhuW (2009) Stability analysis of impulsive switched systems with time delays. Mathematical and Computer Modelling50: 1188–1194.
33.
ZhouBDuanGRLinZL (2008) A parametric Lyapunov equation approach to the design of low gain feedback. IEEE Transactions on Automatic Control53: 1548–1554.
34.
ZhouBLinZLDuanGR (2009) A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems. Automatica45: 238–244.
35.
ZhouBLinZLDuanGR (2011) Lyapunov differential equation approach to elliptical orbital rendezvous with constrained controls. AIAA Journal of Guidance, Control and Dynamics34: 345–358.
