Abstract
This work studies the stochastic stability of Markovian jump linear systems in a communication network-based environment. By modeling quantization density as well as the sensor-to-controller and controller-to-actuator delays as Markov chains, the closed-loop networked control systems are expressed as switched linear systems. The necessary and sufficient conditions of stochastic stability are derived. By solving a set of linear matrix inequalities with matrix inversion constraints, this work presents a three-mode-dependent state-feedback controller. Its control performance is illustrated via a numerical example.
•Random quantization density and time delay are considered in a network environment.•A new model for a networked Markovian jump system is presented.•Sufficient and necessary conditions for a closed-loop system’s stability are given and proved.•A controller depending on a system, delay, and quantization density modes is designed.