Robust H∞ control for nonlinear systems over network: A piecewise analysis method

A piecewise analysis method (PAM) is proposed to investigate the H∞ performance analysis and H∞ control design for nonlinear networked control systems (NNCSs), which are presented in the form of T–S fuzzy model with time-varying input delay. Different from the existing method in dealing with the time-varying delay, the whole variation interval of the delay is divided into two subintervals with equal length. Respecting for the delay belonging each subinterval, new criteria on H∞ performance analysis of the NNCSs are obtained by checking the variation of the derivative of the Lyapunov functional in the two subintervals. Then, criteria for the H∞ controller design are obtained by using the convexity properties of the matrix inequality and some other new analysis techniques, which are shown in terms of nonlinear matrix inequalities and can be solved by using a cone complementarity liberalization method. As application of the derived results, H∞ controller design is carried out for the nonlinear mass-spring system. Discussion shows that the proposed method is less conservative than the existing references.