Quantized repetitive tracking control for Markovian jump nonlinear systems with disturbances and incomplete knowledge of transition rates

Abstract

This work epitomizes the problem of attaining periodic output reference tracking control along with disturbance attenuation for Takagi–Sugeno fuzzy approach based Markov jump systems (TSFMJSs) subject to mismatch quantization, incomplete transition rates and external disturbances. Explicitly, by compiling the disturbance estimates generated by an improved extended state observer (IESO) with a two-dimensional modified repetitive control (2D-MRC) approach, an anti-disturbance tracking control is established for accomplishing the intended tracking goals despite of the disturbances encountered. Further, to restrain the influence of mismatch quantization on the dynamics of the proposed system, a mismatch quantizer is imposed on the developed control protocol. Altogether, a quantized IESO-based anti-disturbance tracking 2D-MRC design is developed to acquire the preferred tracking outcome for the TSFMJS model by retarding the impacts caused by mismatched quantization, unknown transition rates and exogenous disturbances. Typically, by employing certain fuzzy-dependent Lyapunov–Krasovskii functional, the essential stability conditions for the proffered closed-loop system are configured in terms of linear matrix inequality (LMIs). Consequently, the feedback gain parameters are procured from the configured LMIs. Lastly, the theoretical declarations are authenticated by providing two numerical examples, which prevail the efficacy and potential applicability of the organized control protocol.