Discrete-time zeroing neural network for solving time-varying Sylvester-transpose matrix inequation via exp-aided conversion

Time-varying linear matrix equations and inequations have been widely studied in recent years. Time-varying Sylvester-transpose matrix inequation, which is an important variant, has not been fully investigated. Solving the time-varying problem in a constructive manner remains a challenge. This study considers an exp-aided conversion from time-varying linear matrix inequations to equations to solve the intractable problem. On the basis of zeroing neural network (ZNN) method, a continuous-time zeroing neural network (CTZNN) model is derived with the help of Kronecker product and vectorization technique. The convergence property of the model is analyzed. Two discrete-time ZNN models are obtained with the theoretical analyses of truncation error by using two Zhang et al.’s discretization (ZeaD) formulas with different precision to discretize the CTZNN model. The comparative numerical experiments are conducted for two discrete-time ZNN models, and the corresponding numerical results substantiate the convergence and effectiveness of two ZNN discrete-time models