H∞ model reduction for discrete singular Markovian jump systems

2009 ◽  
Vol 223 (7) ◽  
pp. 1017-1025 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Model Reduction ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Bounded Real Lemma ◽  
Singular Markovian Jump Systems ◽  
Discrete Singular Systems ◽  
Jump Systems

The problem of H∞ model reduction is investigated for discrete singular systems with Markovian jump. A stochastic admissibility condition and bounded real lemma (BRL) are established for the discrete singular Markovian jump system in terms of the linear matrix inequality (LMI) approach. Under partial knowledge of the transition probabilities, the strict LMI-based sufficient condition is obtained for the existence of desired reduced-order model. The numerical example is proposed to show the validity of the developed result.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

Stochastic Admissibility for a Class of Nonlinear Singular Markovian Jump Systems with Time-Delay and Partially Unknown Transition Probabilities

2012 ◽  
Vol 235 ◽  
pp. 254-258 ◽  
Author(s):  
Shao Hua Long ◽  
Shou Ming Zhong
Keyword(s):  
Time Delay ◽  
Transition Probabilities ◽  
Functional Method ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Weighting Matrix ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Stochastic Admissibility

The problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities is discussed in this note. The considered singular matrices Er(t) in the discussed system are mode-dependent. By using the free-weighting matrix method and the Lyapunov functional method, a sufficient condition which guarantees the considered system to be stochastically admissible is presented in the form of linear matrix inequalities(LMIs). Finally, a numerical example is given to show the effectiveness of the presented method.

scholarly journals H∞Control of Singular Markovian Jump Systems with Bounded Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongsheng Lin ◽  
Ying Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

This paper discussesH∞control problems of continuous-time and discrete-time singular Markovian jump systems (SMJSs) with bounded transition probabilities. Improved sufficient conditions for continuous-time SMJSs to be regular, impulse free, and stochastically stable withγ-disturbance attenuation are established via less conservative inequality to estimate the transition jump rates, so are the discrete-time SMJSs. With the obtained conditions, the design of a state feedback controller which ensures the resulting closed-loop system to be stochastically admissible and withH∞performance is given in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and the benefits of the proposed approaches.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals H∞ Model Reduction of 2D Markovian Jump System with Roesser Model

2012 ◽  
Vol 6-7 ◽  
pp. 135-142
Author(s):  
Xue Song Han ◽  
Yu Bo Duan
Keyword(s):  
Model Reduction ◽  
Reduced Order Model ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Roesser Model ◽  
Markovian Jump ◽  
Order Model ◽  
Existence Of A Solution ◽  
Reduced Order ◽  
Jump Systems

This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problem of H∞model reduction for a class of linear discrete time 2D Markovian jump systems with state delays in Roesser model which is time-varying and mode-independent. The reduced-order model with the same randomly jumping parameters is proposed which can make the error systems stochastically stable with a prescribed H∞ performance. A sufficient condition in terms of linear matrix inequalitiesSubscript text(LMIs) plus matrix inverse constraints are derived for the existence of a solution to the reduced-order model problems. The cone complimentarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numerical example is given to illustrate the design procedures.

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