Dynamic Output-Feedback Control for Singular Markovian Jump System: LMI Approach

For the dynamic output-feedback stabilization of continuous-time singular Markovian jump systems, this paper introduces the necessary and sufficient condition, whereas the previous research works suggested the sufficient conditions. A special choice of the block entries of Lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities. A numerical example shows the validity of the derived results.

[1]  Robert Sheldon.  Control of Singular Systems with Random Abrupt Changes , 2000 .

[2]  Yonggui Kao,et al.  Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates , 2014, IEEE Transactions on Automatic Control.

[3]  Sung Hyun Kim,et al.  Networked-based robust Hinfinity control design using multiple levels of network traffic , 2009, Autom..

[4]  Robert W. Newcomb,et al.  Some circuits and systems applications of semistate theory , 1989 .

[5]  Peng Shi,et al.  Stochastic stability of Ito differential equations with semi-Markovian jump parameters , 2006, IEEE Transactions on Automatic Control.

[6]  Xiaowu Mu,et al.  Robust finite-time H∞ control of singular stochastic systems via static output feedback , 2012, Appl. Math. Comput..

[7]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[8]  Marco H. Terra,et al.  Nonlinear and Markovian H∞ controls of underactuated manipulators , 2004, IEEE Trans. Control. Syst. Technol..

[9]  Hongsheng Xi,et al.  Markovian-Based Fault-Tolerant Control for Wheeled Mobile Manipulators , 2012, IEEE Transactions on Control Systems Technology.

[10]  Nam Kyu Kwon,et al.  H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities , 2017, Appl. Math. Comput..

[11]  Caixia Liu,et al.  Robust finite-time stabilization of uncertain singular Markovian jump systems , 2012 .

[12]  Andrew A. Goldenberg,et al.  Force and position control of manipulators during constrained motion tasks , 1989, IEEE Trans. Robotics Autom..

[13]  El-Kébir Boukas,et al.  On stability and stabilisation of continuoustime singular markovian switching systems , 2008 .

[14]  Honghai Liu,et al.  Parameter-dependent robust stability for uncertain Markovian jump systems with time delay , 2011, J. Frankl. Inst..

[15]  El-Kébir Boukas,et al.  Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters , 1997 .

[16]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[17]  B. Stott,et al.  Power system dynamic response calculations , 1979, Proceedings of the IEEE.

[18]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[19]  E. Uezato,et al.  Strict LMI conditions for stability, robust stabilization, and H/sub /spl infin// control of descriptor systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Wei Cheng,et al.  Observer-Based Finite-Time H∞ Control of Singular Markovian Jump Systems , 2012, J. Appl. Math..

[21]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[22]  J. Raouf,et al.  Stochastic output feedback controller for singular Markovian jump systems with discontinuities , 2009 .

[23]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[24]  John S. Baras,et al.  A linear distributed filter inspired by the Markovian jump linear system filtering problem , 2012, Autom..

[25]  Huai-Ning Wu,et al.  H∞ fuzzy control design of discrete‐time nonlinear active fault‐tolerant control systems , 2009 .

[26]  Xudong Zhao,et al.  New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays , 2010, J. Frankl. Inst..