Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities

This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and randomly occurring nonlinearities obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The mixed time delays consist of both the discrete and the distributed delays. The time-varying delays are allowed in state. By employing the idea of delay fractioning and constructing a new Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving a certain semidefinite programming problem. A full-state feedback SMC law is designed to guarantee the reaching condition. A simulation example is given to demonstrate the effectiveness of the proposed SMC scheme.

[1]  Xuerong Mao,et al.  SMC design for robust H∞ control of uncertain stochastic delay systems , 2010, Autom..

[2]  Dimitri Peaucelle,et al.  Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation , 2007, Autom..

[3]  Bijnan Bandyopadhyay,et al.  Output Feedback Sliding-Mode Control for Uncertain Systems Using Fast Output Sampling Technique , 2006, IEEE Transactions on Industrial Electronics.

[4]  May-Win L. Thein,et al.  Quasi-Continuous Higher Order Sliding-Mode Controllers for Spacecraft-Attitude-Tracking Maneuvers , 2010, IEEE Transactions on Industrial Electronics.

[5]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[6]  Yuanqing Xia,et al.  Design of Static Output Feedback Sliding Mode Control for Uncertain Linear Systems , 2010, IEEE Transactions on Industrial Electronics.

[7]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[8]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[9]  Xinghuo Yu,et al.  Sliding-Mode Control With Soft Computing: A Survey , 2009, IEEE Transactions on Industrial Electronics.

[10]  Arindam Ghosh,et al.  Multiband Hysteresis Modulation and Switching Characterization for Sliding-Mode-Controlled Cascaded Multilevel Inverter , 2010, IEEE Transactions on Industrial Electronics.

[11]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[12]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[13]  B. A. Woodyatt,et al.  Fault Signatures Obtained From Fault Implant Tests on an F404 Engine , 1992 .

[14]  Han Ho Choi,et al.  LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems , 2007, IEEE Transactions on Automatic Control.

[15]  Luis Martinez-Salamero,et al.  Two-Loop Digital Sliding Mode Control of DC–DC Power Converters Based on Predictive Interpolation , 2011, IEEE Transactions on Industrial Electronics.

[16]  Christopher Edwards,et al.  On Output Tracking Using Dynamic Output Feedback Discrete-Time Sliding Mode Controllers , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Muhammed Fazlur Rahman,et al.  Sensorless Sliding-Mode MTPA Control of an IPM Synchronous Motor Drive Using a Sliding-Mode Observer and HF Signal Injection , 2010, IEEE Transactions on Industrial Electronics.

[18]  Teresa Orlowska-Kowalska,et al.  Implementation of a Sliding-Mode Controller With an Integral Function and Fuzzy Gain Value for the Electrical Drive With an Elastic Joint , 2010, IEEE Transactions on Industrial Electronics.

[19]  Xinghuo Yu,et al.  On the Discrete-Time Integral Sliding-Mode Control , 2007, IEEE Transactions on Automatic Control.

[20]  Yuanqing Xia,et al.  Sliding mode control of uncertain linear discrete time systems with input delay , 2007 .

[21]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[22]  M. Yan,et al.  Robust discrete-time sliding mode control for uncertain systems with time-varying state delay , 2008 .