Abstract. This paper considers a linear discrete time-invariant system with multiplicative noise and a control input under an external disturbance from a special class. The plant’s dynamics are described in the state space. The class of external disturbances contains a set of stationary Gaussian sequences with a bounded mean anisotropy. The anisotropic norm of the closed-loop control system is chosen as the performance criterion. It is required to design a dynamic link-based control scheme under which the anisotropic norm of the closed-loop control system will be bounded by the minimum possible threshold. At the first stage of solving this problem, the controller’s dynamics are written out and the plant under consideration is augmented. The boundedness criterion of the anisotropic norm in terms of matrix inequalities is used to derive sufficient conditions for the existence of a solution of a convex optimization problem to minimize the upper bound of the anisotropic norm. A special change of variables is performed in the resulting inequalities to eliminate the nonlinear dependence on the unknown controller matrices. After a linearizing inversible change of variables, the optimization problem is solved numerically using standard methods. At the last stage, the desired controller matrices are calculated in the state space to ensure the bounded anisotropic norm of the closed-loop control system.
Keywords: linear discrete time-invariant systems, anisotropy-based theory, dynamic control, LMI, convex optimization.
Acknowledgments. This work was supported by the Russian Science Foundation, project no. 24-21-20055.
Yurchenkov, A.V., Dynamic Anisotropy-Based Controller Design for Time-Invariant Systems with Multiplicative Noise. Control Sciences 1, 25–33 (2025).
Dynamic Anisotropy-Based Controller Design for Time-Invariant Systems with Multiplicative Noise