scholarly journals Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Yanfeng Zhao ◽  
Jihong Shen ◽  
Dongyan Chen
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Estimation Error ◽  
Estimation Method ◽  
Genetic Regulatory Networks ◽  
Independent Random Variables ◽  
Linear Matrix ◽  
Time Varying ◽  
State Estimator ◽  
Randomly Occurring Uncertainties

We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with time-varying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a Lyapunov-Krasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.

Exponential state estimation for discrete-time switched genetic regulatory networks with random delays

2014 ◽  
Vol 92 (9) ◽  
pp. 976-986 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel ◽  
Hongye Su
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Regulatory Networks ◽  
Estimation Error ◽  
Average Dwell Time ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
State Estimator ◽  
Exponentially Stable

This paper is concerned with the problem of state estimator design for a class of discrete-time switched genetic regulatory networks (GRNs) with random time delays. The involved time delays are assumed to be randomly time-varying and are modeled by introducing Bernoulli distributed sequences. By using a piecewise Lyapunov–Krasovskii functional together with the linear matrix inequality (LMI) approach, we design a delay-distributed dependent state estimator such that the estimation error system is globally exponentially stable. Further, a class of switching signals specified by the average dwell time is identified to guarantee the exponential state estimation. All the conditions are established in the framework of LMIs, which can easily be solved by using standard numerical software. If a set of LMIs are feasible, then the desired state estimator can be obtained. Finally, a numerical example with simulation result is provided for the GRN model to illustrate the applicability and usefulness of the obtained theory.

scholarly journals New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Yanfeng Zhao ◽  
Jihong Shen ◽  
Dongyan Chen
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Stochastic Disturbances ◽  
Weighting Matrix ◽  
Improved Stability ◽  
Theoretical Results

We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results.

Robust stabilization and H∞ control for discrete-time stochastic genetic regulatory networks with time delays

2012 ◽  
Vol 90 (10) ◽  
pp. 939-953 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Robust Stabilization ◽  
Genetic Regulatory Networks ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Stochastic Genetic Regulatory Networks

This paper presents some novel results on robust stabilization and H∞ control design for a class of uncertain discrete-time stochastic genetic regulatory networks (GRNs) with time-varying delays. The GRNs under consideration are subject to stochastic noise, time-varying, and norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional that contains some novel triple summation terms, we propose a state feedback gene controller to guarantee that the considered GRN is mean-square asymptotically stable about its equilibrium point for all admissible uncertainties. The other issue is to design a H∞ feedback gene controller so that the GRN is robustly stable with a prescribed H∞ disturbance attenuation level for all admissible uncertainties and for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, the control scheme has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained results.

New robust passivity criteria for discrete-time genetic regulatory networks with Markovian jumping parameters

2012 ◽  
Vol 90 (2) ◽  
pp. 107-118 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Equilibrium Points ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping ◽  
Time Varying Delay ◽  
The Matrix ◽  
Inequality Technique

In this paper, we present some novel results for robust passivity of a class of uncertain discrete-time Markovian jumping genetic regulatory networks (GRNs) with time-varying delays. By constructing a new set of Lyapunov–Krasovskii functionals, together with the matrix inequality technique, we provide a new set of results for the passiveness, and also ensure the mean-square asymptotical stability (internally) of the considered GRNs about their equilibrium points for all time delays satisfying both the lower bound and upper bound of the interval time-varying delay. Further, the obtained results are extended to deal with the robust passiveness of the considered GRNs for all admissible uncertainties. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, numerical examples with simulation results are provided for the GRN model to illustrate the applicability and usefulness of the theory.

scholarly journals Optimal guaranteed cost filtering for Markovian jump discrete-time systems

2004 ◽  
Vol 2004 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Peng Shi
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
State Estimator ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Discrete Time Systems ◽  
Linear State ◽  
Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

scholarly journals State Observer Design for Delayed Genetic Regulatory Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Ping Tian ◽  
Zhi-Jun Wang ◽  
Amin Mohammadbagheri ◽  
Fang-Xiang Wu
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Estimation Error ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Observer Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
Internal States

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

2016 ◽  
Vol 71 (4) ◽  
pp. 289-304 ◽  
Author(s):  
R. Sakthivel ◽  
M. Sathishkumar ◽  
B. Kaviarasan ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Interval ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

scholarly journals An advanced delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays

2018 ◽  
Vol 23 (6) ◽  
pp. 803-829 ◽  
Author(s):  
Selvakumar Pandiselvi ◽  
Raja Ramachandran ◽  
Jinde Cao ◽  
Grienggrai Rajchakit ◽  
Aly R. Seadawy ◽  
...  
Keyword(s):  
Regulatory Networks ◽  
Convex Combination ◽  
Genetic Regulatory Networks ◽  
Distributed Delays ◽  
Combination Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Theoretical Concepts ◽  
Delay Dependent

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts.

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