This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method) is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degreen, the corresponding transformation matrix of ordernexists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.
This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obtained for leaderless PDE-ODEMASs to achieve leaderless consensus. Furthermore, a consensus controller in the leader-following PDE-ODEMAS is designed and the corresponding coupling strengths are obtained to ensure the leader-following consensus. Two examples show the effectiveness of the proposed methods.
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