Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
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R. Sakthivel
,
M. Sathishkumar
Abstract
This 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.
Acknowledgments
The work of S. Marshal Anthoni was supported by the NBHM/DAE under grant No. 2/48(4)/2013/NBHM(R.P)/R&D II/687. The work of M. Sathishkumar was supported by Rajiv Gandhi National Fellowship (RGNF), UGC, New Delhi, India [grant no. F1-17.1/2015-16/RGNF-2015-17-SC-TAM-18857/(SA-III/Website), dated: 09-01-2016].
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©2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
