Stochastic stabilization of singular systems with Markovian switchings

This paper studies the stochastic stabilization problem for a class of singular Markovian jump system. The aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular Markovian jump system (SMJS). A new kind of stochastic controller only in the diffusion part is proposed such that the closed-loop system has a unique solution and is almost surely exponentially admissible. New sufficient condition for the existence of such a controller is given as linear matrix inequalities (LMIs). Based on this, more extensions to transition probability matrix (TPM) with elements partially unknown and system states partially observable are developed. A numerical example is used to demonstrate the effectiveness of the proposed methods.

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

[2]  Xuerong Mao,et al.  Stabilization and Destabilization of Nonlinear Differential Equations by Noise , 2008, IEEE Transactions on Automatic Control.

[3]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[4]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[5]  Xuerong Mao,et al.  Stochastic stabilization and destabilization , 1994 .

[6]  Gang George Yin,et al.  Stabilization and destabilization of hybrid systems of stochastic differential equations , 2007, Autom..

[7]  James Lam,et al.  Robust filtering for discrete-time Markovian jump delay systems , 2004, IEEE Signal Processing Letters.

[8]  El Kebir Boukas.  Manufacturing systems: LMI approach , 2006, IEEE Transactions on Automatic Control.

[9]  Chunyu Yang,et al.  Exponential H ∞  filtering for singular systems with Markovian jump parameters , 2013 .

[10]  Peter C. Müller,et al.  Linear mechanical descriptor systems: Identification, analysis and design. , 1997 .

[11]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[12]  Feiqi Deng,et al.  Stochastic stabilization of hybrid differential equations , 2012, Autom..

[13]  Francesco Martinelli,et al.  Optimality of a Two-Threshold Feedback Control for a Manufacturing System With a Production Dependent Failure Rate , 2007, IEEE Transactions on Automatic Control.

[14]  Wei Xing Zheng,et al.  Generalized H2 fault detection for two-dimensional Markovian jump systems , 2012, Autom..

[15]  El-Kébir Boukas,et al.  Control of Singular Systems with Random Abrupt Changes , 2008 .

[16]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[17]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[18]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

[19]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[20]  Ashish Tiwari,et al.  Symbolic Systems Biology: Hybrid Modeling and Analysis of Biological Networks , 2004, HSCC.

[21]  Lirong Huang.  Stochastic stabilization and destabilization of nonlinear differential equations , 2013, Syst. Control. Lett..

[22]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[23]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[24]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[25]  H. Su,et al.  H∞ filtering for singular Markovian jump systems with time delay , 2010 .

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

[27]  Liangjian Hu,et al.  Almost sure exponential stabilisation of stochastic systems by state-feedback control , 2008, Autom..

[28]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[29]  João Pedro Hespanha,et al.  Stochastic Hybrid Systems: Application to Communication Networks , 2004, HSCC.

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

[31]  Qingling Zhang,et al.  Robust control of uncertain singular stochastic systems with Markovian switching via proportional–derivative state feedback , 2012 .

[32]  Qingling Zhang,et al.  Analysis and Design of Singular Markovian Jump Systems , 2014 .

[33]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[34]  Xuerong Mao,et al.  Stability of Singular Stochastic Systems With Markovian Switching , 2011, IEEE Transactions on Automatic Control.

[35]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[36]  Xuerong Mao,et al.  On Almost Sure Stability of Hybrid Stochastic Systems With Mode-Dependent Interval Delays , 2010, IEEE Transactions on Automatic Control.

[37]  Guoliang Wang,et al.  Dissipative control for singular Markovian jump systems with time delay , 2012 .

[38]  Peng Shi,et al.  Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $ , 2010, IEEE Transactions on Automatic Control.

[39]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

[40]  Magdi S. Mahmoud,et al.  Dissipativity analysis and design for uncertain Markovian jump systems with time-varying delays , 2013, Appl. Math. Comput..

[41]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[42]  James Lam,et al.  Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions , 2010, IEEE Transactions on Automatic Control.

[43]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[44]  Huijun Gao,et al.  Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach , 2014, Autom..

[45]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.

[46]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[47]  Hao Shen,et al.  Finite-time reliable L 2 - Lα/Hα control for Takagi-Sugeno fuzzy systems with actuator faults , 2014 .

[48]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..