## Novel delay-dependent stability conditions for a class of MIMO networked control systems with nonlinear perturbation.(English)Zbl 1136.93409

Summary: This paper considers the problem of delay-dependent stability criteria for a class of Multi-Input and Multi-Output (MIMO) networked control systems with nonlinear perturbation. Due to many independent sensors and actuators existed in the MIMO networked control systems, a distributed time delays networked control systems with structured uncertainties and external nonlinear perturbation is proposed in this paper. Based on Lyapunov stability theory combined with the descriptor system approach and Linear Matrix Inequalities (LMIs) techniques, some novel and improved sufficient conditions are derived to the delay-dependent stability of these systems. By solving a convex optimization problem of the LMI, the maximum upper bound of the allowable delay can be obtained. Compared to the existing criterions on this aspect, the proposed criteria gives a much less conservative maximum allowable delay bound. Numerical examples and simulations illustrate that our conditions are feasible and are less conservative than previous ones.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93A15 Large-scale systems 90C25 Convex programming
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