A trilinear estimate with application to the perturbed nonlinear Schrödinger equations with the Kerr law nonlinearity

Parametric design to reduced-order functional observer for linear time-varying systems

“…Then substitute corresponding matrices with the ones defined in system ( 22), and we can get equations ( 25)- (29). The proof is completed.…”

“…Combining equations ( 25)-( 29) yields (31). Particular, the matrix M(t) is determined by (29), and it is solvable if and only if rank T1 (t)…”

“…The use of some mathematical methods, including matrix equations, nonlinear equations play a vital role in the establishment and application of control theory and system models. [28][29][30][31] Zhou and Duan, 32 Duan, 33 Gu and Zhang, 34,35 Gu et al 36,37 studied the fully parameterized solution of homogeneous generalized Sylvester equations (GSEs), and its application in typical control problems such as characteristic structure configuration and observer design, which laid a solid theoretical foundation for control system design. Based on the results of the fully parameterized solution of GSEs proposed in Zhou and Duan, 32 this study investigates the problem of state reconstruction for LTV models.…”