This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results.
Skip Nav Destination
Article navigation
October 2015
Research-Article
Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties
S. Dharani,
S. Dharani
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
Search for other works by this author on:
R. Rakkiyappan,
R. Rakkiyappan
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Search for other works by this author on:
Jinde Cao
Jinde Cao
Department of Mathematics and
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Search for other works by this author on:
S. Dharani
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com
R. Rakkiyappan
Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com
Jinde Cao
Department of Mathematics and
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 15, 2014; final manuscript received June 5, 2015; published online July 21, 2015. Assoc. Editor: Umesh Vaidya.
J. Dyn. Sys., Meas., Control. Oct 2015, 137(10): 101008
Published Online: July 21, 2015
Article history
Received:
August 15, 2014
Revision Received:
June 5, 2015
Citation
Dharani, S., Rakkiyappan, R., and Cao, J. (July 21, 2015). "Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties." ASME. J. Dyn. Sys., Meas., Control. October 2015; 137(10): 101008. https://doi.org/10.1115/1.4030800
Download citation file:
Get Email Alerts
Dynamic Obstacle Avoidance Strategy for High-Speed Vehicles Via Constrained Model Predictive Control and Improved Artificial Potential Field
J. Dyn. Sys., Meas., Control (July 2025)
An Adaptive Sliding-Mode Observer-Based Fuzzy PI Control Method for Temperature Control of Laser Soldering Process
J. Dyn. Sys., Meas., Control
Fault detection of automotive engine system based on Canonical Variate Analysis combined with Bhattacharyya Distance
J. Dyn. Sys., Meas., Control
Related Articles
Stochastic Finite-Time Stabilization for a Class of Nonlinear Markovian Jump Stochastic Systems With Impulsive Effects
J. Dyn. Sys., Meas., Control (April,2015)
Robust Control of Uncertain Nonlinear Systems: A Nonlinear DOBC Approach
J. Dyn. Sys., Meas., Control (July,2016)
An Online Tuning Method for Robust Control of Multivariable Nonlinear Processes With Nonanalytical Modules and Time Delay
J. Dyn. Sys., Meas., Control (April,2017)
Constrained Robust Control for Spacecraft Attitude Stabilization Under Actuator Delays and Faults
J. Dyn. Sys., Meas., Control (May,2017)
Related Proceedings Papers
Related Chapters
Fault-Tolerant Control of Sensors and Actuators Applied to Wind Energy Systems
Electrical and Mechanical Fault Diagnosis in Wind Energy Conversion Systems
GA Based Competitive Multi-Agent Controller for Nonlinear System
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Dynamic Simulations to Become Expert in Order to Set Fuzzy Rules in Real Systems
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)