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This paper considers a co-design problem for industrial networked controlsystems to ensure both the stability and efficiency properties of such systems.The assurance of such properties is particularly challenging due to the factthat wireless communications in industrial environments are not only subject toshadow fading but also stochastically correlated with their surroundingenvironments. To address such challenges, this paper first introduces a novelstate-dependent Markov channel (SD-MC) model that explicitly captures thestate-dependent features of industrial wireless communication systems bydefining the proposed model's transition probabilities as a function of bothits environment's states and transmission power. Under the proposed channelmodel, sufficient conditions on Maximum Allowable Transmission Interval (MATI)are presented to ensure both asymptotic stability in expectation and almostsure asymptotic stability properties of a continuous nonlinear control systemwith state-dependent fading channels. Based on such conditions, the co-designproblem is then formulated as a constrained polynomial optimization problem(CPOP), which can be efficiently solved using semidefinite programming methodsfor the case of a two-state state dependent Markovian channel. The solutions tosuch a CPOP represent optimal control and power strategies that optimize theaverage expected joint costs in an infinite time horizon while still respectthe stability constraints. For a general SD-MC model, this paper further showsthat sub-optimal solutions can be obtained from linear programming formulationsof the considered CPOP. Simulation results are given to illustrate the efficacyof the proposed co-design scheme.

Co-design of Optimal Transmission Power and Controller for Networked Control Systems Under State-dependent Markovian Channels