Neutrosophic state feedback design method for SISO neutrosophic linear systems

Abstract

The indeterminacy of parameters in actual control systems is inherent property because some parameters in actual control systems are changeable rather than constants in some cases, such as manufacturing tolerances, aging of main components, and environmental changes, which present an uncertain threat to actual control systems. Therefore, these indeterminate parameters can affect the control behavior and performance. Then, a neutrosophic number (NN) z = d + eI consists of its determinate term d and its indeterminate term eI for d, e ∈ R (R is all real numbers and I denotes indeterminacy). In fact, NN implies a changeable interval depending on the indeterminate range of I ∈ [IL, IU] and easily expresses determinate and/or indeterminate information. Unfortunately, NNs are not introduced into the modeling, analysis, and design of uncertain control systems with interval/determinate parameters in existing literature so far. To develop a new neutrosophic design method, this study firstly introduces neutrosophic state space models and the neutrosophic controllability and observability in indeterminate linear systems. Then, a neutrosophic state feedback design method is established for achieving a desired closed-loop state equation or a desired control ratio for single-input single-output (SISO) neutrosophic linear systems. Finally, the proposed control design method is used for a numerical example with NN parameters, and the simulation results demonstrate that the designed state feedback control system can reach the desired system tracking performance requirements. Meanwhile, the obtained state feedback design result demonstrates its effectiveness and robustness.