Mode-mismatched estimator design for Markov jump genetic regulatory networks with random time delays

Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

Improved stability and stabilization design for networked control systems using new quadruple-integral functionals

This paper investigates stability analysis and stabilization for networked control systems. By a refined delay decomposition approach, slightly different Lyapunov-Krasovskii functionals (LKFs) with quadruple-integral terms and augmented vectors containing triple-integral forms of state are constructed. New integral inequalities are proposed to estimate the cross terms from derivatives of the LKFs, which can be proved to offer tighter bounds than what the Jensen one produces theoretically. Moreover, the non-strictly proper rational functions in deriving process are fully handled via reciprocally convex approach. A state feedback controller design approach is also developed. Numerical examples and applications to practical power and oscillator systems demonstrate the superiority of the proposed criteria in conservatism reduction compared to some existing ones.