Research Papers

Gain-Scheduled H Control for Linear Parameter Varying Stochastic Systems

[+] Author and Article Information
Cheung-Chieh Ku

Department of Marine Engineering,
National Taiwan Ocean University,
Keelung 202, Taiwan
e-mail: ccku@mail.ntou.edu.tw

Cheng-I Wu

Department of Marine Engineering,
National Taiwan Ocean University,
Keelung 202, Taiwan
e-mail: hhhhhhhhhh10622@yahoo.com.tw

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 24, 2014; final manuscript received July 9, 2015; published online August 20, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(11), 111012 (Aug 20, 2015) (12 pages) Paper No: DS-14-1497; doi: 10.1115/1.4031059 History: Received November 24, 2014

In this paper, a gain-scheduled controller design method is proposed for linear parameter varying (LPV) stochastic systems subject to H performance constraint. Applying the stochastic differential equation, the stochastic behaviors of system are described via multiplicative noise terms. Employing the gain-scheduled design technique, the stabilization problem of LPV stochastic systems is discussed. Besides, the H attenuation performance is employed to constrain the effect of external disturbance. Based on the Lyapunov function and Itô's formula, the sufficient conditions are derived to propose the stability criteria for LPV stochastic systems. The derived sufficient conditions are converted into linear matrix inequality (LMI) problems that can be solved by using convex optimization algorithm. Through solving these conditions, the gain-scheduled controller can be obtained to guarantee asymptotical stability and H performance of LPV stochastic systems. Finally, numerical examples are provided to demonstrate the applications and effectiveness of the proposed controller design method.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Johansen, T. A. , Hunt, K. J. , and Fritz, H. , 1998, “A Software Environment for Gain Scheduled Controller Design,” IEEE Control Syst., 18(2), pp. 48–60. [CrossRef]
Silvestre, C. , and Pascoal, A. , 2004, “Control of the INFANTE AUV Using Gain Scheduled Static Output Feedback,” Control Eng. Pract., 12(12), pp. 1501–1509. [CrossRef]
Johansen, T. A. , Petersen, I. , Kalkkuhl, J. , and Lüdemann, J. , 2003, “Gain-Scheduled Wheel Slip Control in Automotive Brake Systems,” IEEE Trans. Control Syst. Technol., 11(6), pp. 799–811. [CrossRef]
Yue, T. , Wang, L. , and Ai, J. , 1998, “Gain Self-Scheduled H Control for Morphing Aircraft in the Wing Transition Process Based on an LPV Model,” Chin. J. Aeronaut., 26(4), pp. 909–917. [CrossRef]
Yoon, M. G. , Ugrinovskii, V. A. , and Pszczel, M. , 2007, “Gain-Scheduling of Minimax Optimal State-Feedback Controllers for Uncertain LPV Systems,” IEEE Trans. Autom. Control, 52(2), pp. 311–317. [CrossRef]
Blanchini, F. , Casagrande, D. , Miani, S. , and Viaro, U. , 2010, “Stable LPV Realization of Parametric Transfer Functions and Its Application to Gain-Scheduling Control Design,” IEEE Trans. Autom. Control, 55(10), pp. 2271–2281. [CrossRef]
Montagner, V. F. , Oliveira, R. C. L. F. , Leite, V. J. S. , and Peres, P. L. D. , 2005, “LMI Approach for H Linear Parameter-Varying State Feedback Control,” IEE Proc. Control Theory Appl., 152(2), pp. 195–201. [CrossRef]
Oliveira, R. C. L. F. , de Oliveira, M. C. , and Peres, P. L. D. , 2009, “Special Time-Varying Lyapunov Function for Robust Stability Analysis of Linear Parameter Varying Systems With Bounded Parameter Variation,” IET Control Theory Appl., 3(10), pp. 1448–1461. [CrossRef]
Liu, L. , Wei, X. , and Liu, X. , 2007, “LPV Control for the Air Path System of Diesel Engines,” IEEE International Conference on Control and Automation, Guangzhou, China, May 30–June 1, pp. 873–878.
Daafouz, J. , Bernussou, J. , and Geromel, J. C. , 2008, “On Inexact LPV Control Design of Continuous-Time Polytopic Systems,” IEEE Trans. Autom. Control, 53(7), pp. 1674–1678. [CrossRef]
Wu, F. , and Grigoriadis, K. M. , 2001, “LPV Systems With Parameter-Varying Time Delays: Analysis and Control,” Automatica, 37(2), pp. 221–229. [CrossRef]
Sloth, C. , Esbensen, T. , and Stoustrup, J. , 2011, “Robust and Fault-Tolerant Linear Parameter-Varying Control of Wind Turbines,” Mechatronics, 21(4), pp. 645–659. [CrossRef]
Chisci, L. , Falugi, P. , and Zappa, G. , 2003, “Set-Point Tracking for a Class of Constrained Nonlinear Systems With Application to a CSTR,” 42nd IEEE Conference on Decision and Control, Maui, HI, Dec. 9–12, Vol. 4, pp. 3930–3935.
Yaesh, I. , Boyarski, S. , and Shaked, U. , 2003, “Probability-Guaranteed Robust H Performance Analysis and State-Feedback Design,” Syst. Control Lett., 48(5), pp. 351–364. [CrossRef]
Jeung, E. T. , Kim, J. H. , and Park, H. B. , 1998, “ H -Output Feedback Controller Design for Linear Systems With Time-Varying Delayed State,” IEEE Trans. Autom. Control, 43(7), pp. 971–974. [CrossRef]
Gahinet, P. , Apkarian, P. , and Chilali, M. , 1996, “Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty,” IEEE Trans. Autom. Control, 41(3), pp. 436–442. [CrossRef]
Lee, S. H. , and Lim, J. T. , 2000, “Switching Control of H Gain Scheduled Controllers in Uncertain Nonlinear Systems,” Automatica, 36(7), pp. 1067–1074. [CrossRef]
Qin, W. , and Wang, Q. , 2007, “Using Stochastic Linear-Parameter-Varying Control for CPU Management of Internet Servers,” 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 3824–3829.
Liu, J. , Hu, Y. , and Lin, Z. , 2013, “State-Feedback H Control for LPV System Using T-S Fuzzy Linearization Approach,” Math. Probl. Eng., 2013, p. 169454.
Eli, G. , Uri, S. , and Isaac, Y. , 2005, H Control and Estimation of State-Multiplicative Linear Systems, Springer, London.
Dragan, V. , Morozan, T. , and Stoica, A. M. , 2013, Mathematical Methods in Robust Control of Linear Stochastic Systems, Springer, New York.
Allen, E. , 2007, Modelling With Itô Stochastic Differential Equations, Springer, Lubbock, TX.
Ghaoui, L. E. , 1995, “State-Feedback Control of Systems With Multiplicative Noise Via Linear Matrix Inequalities,” Syst. Control Lett., 24(3), pp. 223–228. [CrossRef]
Phillis, Y. A. , 1989, “Estimation and Control of Systems With Unknown Covariance and Multiplicative Noise,” IEEE Trans. Autom. Control, 34(10), pp. 1075–1078. [CrossRef]
Mao, X. , Koroleva, N. , and Rodkina, A. , 1998, “Robust Stability of Uncertain Stochastic Differential Delay Equations,” Syst. Control Lett., 35(5), pp. 325–336. [CrossRef]
Fang, X. , and Wang, J. , 2008, “Stochastic Observer-Based Guaranteed Cost Control for Networked Control Systems With Packet Dropouts,” IET Control Theory Appl., 2(11), pp. 980–989. [CrossRef]
Chen, Y. L. , and Chen, B. S. , 1994, “Minimax Robust Deconvolution Filters Under Stochastic Parametric and Noise Uncertainties,” IEEE Trans. Signal Process., 42(1), pp. 32–45. [CrossRef]
Ugrinovskii, V. A. , and Petersen, I. R. , 2001, “Robust Stability and Performance of Stochastic Uncertain Systems on an Infinite Time Interval,” Syst. Control Lett., 44(4), pp. 291–308. [CrossRef]
Xu, S. , and Chen, T. , 2004, “ H Output Feedback Control for Uncertain Stochastic System With Time-Varying Delays,” Automatica, 40(12), pp. 2091–2098.
Ma, L. , Wang, Z. , Bo, Y. , and Guo, Z. , 2011, “A Game Theory Approach to Mixed H 2/H Control for a Class of Stochastic Time-Varying Systems With Randomly Occurring Nonlinearities,” Syst. Control Lett., 60(12), pp. 1009–1015. [CrossRef]
Liu, J. , Hu, Y. , Chang, T. , Yang, T. , Lin, Z. , and Li, M. , 2014, “Stability and Stabilization of Stochastic Linear Parameter Varying T-S Fuzzy System,” 19th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, pp. 40–45.
Boyd, S. , Ghaoui, L. E. , Feron, E. , and Balakrishnan, V. , 1994, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia.


Grahic Jump Location
Fig. 1

Responses of example 1 (Theorem 1)

Grahic Jump Location
Fig. 2

Responses of example 1 (Theorem 2)

Grahic Jump Location
Fig. 3

Responses for x1(t) of example 2

Grahic Jump Location
Fig. 4

Responses for x2(t) of example 2

Grahic Jump Location
Fig. 5

Responses for x3(t) of example 2



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In