On Feedback Control of Discrete Chaotic Multivalued Systems with Tent Circuit Models

Many real-world phenomena can be more accurately described by multivalued rather than single-valued mappings, which provide richer frameworks for modeling uncertainty and nonlinearity. In this work, we investigate chaos control for one-dimensional discrete multivalued dynamical systems by introducing a one-step feedback mechanism based on fixed point iteration theory. The proposed framework extends classical Mann-type iterations to the multivalued setting and provides explicit contraction conditions and computable stability intervals for the growth-rate parameters. Within these intervals, the feedback operator guarantees local attractivity, thereby transforming unstable fixed points and periodic structures to stable ones. To illustrate the applicability of the method, we focus on the multivalued tent map, a prototypical chaotic system. Numerical experiments performed in MATLAB confirm that under the proposed feedback mechanism, chaotic trajectories converge to stable fixed points and unstable periodic orbits are stabilized within the predicted parameter ranges. The bifurcation diagrams further demonstrate that the period-doubling route to chaos is stabilized, with chaotic windows replaced by stable regimes in exact agreement with the theoretical predictions. Finally, as a practical engineering application, the methodology is extended to tent-based electronic circuit models that are widely used in integrated circuit and microchip design. By incorporating the multivalued feedback control system, we demonstrate that chaotic oscillations in such circuits can be effectively stabilized, ensuring stable dynamical behavior. In this way, the results establish a rigorous and constructive framework that bridges abstract multivalued fixed point theory with concrete applications in engineering, advancing both theoretical depth and practical relevance in the field of chaos control.