Observer-Based Robust H∞ Control for Stochastic Markov Jump Delay Systems Through Dual Adaptive Sliding Mode Approach

This study presents an approach to enhancing the robustness of H∞ control in Ito^-type stochastic Markov jump systems, addressing uncertainties in parameters, time-varying delays, and nonlinear perturbations. In this study, the nonlinearities are not exactly known, so an adaptive control strategy is employed. Firstly, an adaptive state observer of full dimension is constructed along with the derivation of error dynamics. Subsequently, different from traditional methods, two linear sliding surfaces are designed, respectively, for the state observer system and error dynamics, resulting in two sliding mode dynamics. Secondly, by employing the linear matrix inequality (LMI) method, sufficient conditions are established to ensure mean-square exponential stability of the closed-loop systems, including observer sliding mode dynamics and error sliding mode dynamics, along with an H∞ attenuation performance index γ. Thirdly, adaptive sliding mode controllers are proposed, ensuring the finite-time arrival and maintenance of the established sliding surfaces. Finally, the efficacy of the derived outcomes is illustrated utilizing the Tunnel Diode circuit model as a demonstrative case study. In this example, the system’s state responses, sliding surface functions, control input, and estimated parameters are simulated under different operating modes and external disturbances. The results demonstrate that the proposed adaptive sliding mode control strategy ensures faster and better convergence compared to error dynamics without control.