Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Sathananthan, S.; Beane, Carlos; Keel, L.H.

doi:10.1080/07362990902976249

Cited by 3 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the study of MJSs with time delays has received considerable attention in recent years. The results on such systems can be classified into two types: delayindependent results [9,10] and delay-dependent ones [11][12][13][14][15][16][17][18][19]. Usually, the delay-dependent conditions are less conservative than delay-independent ones, especially when the size of the delay is small.…”

Section: Introductionmentioning

confidence: 99%

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay

Lin

Fei

Shen

et al. 2010

Proceedings of the Institution of Mechanical Engineers, Part I:

View full text Add to dashboard Cite

This paper is concerned with exponential estimates and H∞ control for a class of singular Markovian jump systems with interval time-varying delay. By constructing an appropriate Lyapunov-Krasovskii functional and using some algebraic techniques, a sufficient condition, which does not only guarantee the regularity, absence of impulses, and mean square exponential stability but also gives the estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). A bounded real lemma is also developed. Based on these, a state-feedback controller which makes the closed-loop system stochastically exponentially admissible with a guaranteed H∞ noise-attenuation performance and a prescribed lower bound of the decay rate is designed by employing the LMI technique. Numerical examples are provided to illustrate the effectiveness of the proposed design methods.

show abstract

Section: Introductionmentioning

confidence: 99%

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay

Lin

Fei

Shen

et al. 2010

Proceedings of the Institution of Mechanical Engineers, Part I:

View full text Add to dashboard Cite

show abstract

Robust stability and stabilization of a class of nonlinear discrete time stochastic systems: An LMI approach

Sathananthan

Knap

Strong

et al. 2012

Applied Mathematics and Computation

View full text Add to dashboard Cite

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

Sathananthan

Knap

Keel

2013

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

A problem of robust guaranteed cost control of stochastic discrete-time systems with parametric uncertainties under Markovian switching is considered. The control is simultaneously applied to both the random and the deterministic components of the system. The noise (the random) term depends on both the states and the control input. The jump Markovian switching is modeled by a discrete-time Markov chain and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Using linear matrix inequalities (LMIs) approach, the robust quadratic stochastic stability is obtained. The proposed control law for this quadratic stochastic stabilization result depended on the mode of the system. This control law is developed such that the closed-loop system with a cost function has an upper bound under all admissible parameter uncertainties. The upper bound for the cost function is obtained as a minimization problem. Two numerical examples are given to demonstrate the potential of the proposed techniques and obtained results.

show abstract

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Cited by 3 publications

References 23 publications

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay

Robust stability and stabilization of a class of nonlinear discrete time stochastic systems: An LMI approach

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

Contact Info

Product

Resources

About

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Cited by 3 publications

References 23 publications

Exponential estimates and H∞ control for singular Markovian jump systems with interval time-varying delay

Exponential estimates and H∞ control for singular Markovian jump systems with interval time-varying delay

Robust stability and stabilization of a class of nonlinear discrete time stochastic systems: An LMI approach

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

Contact Info

Product

Resources

About

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay

Exponential estimates and H_∞ control for singular Markovian jump systems with interval time-varying delay