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A new reliable structure-preserving algorithm for computingH∞norm of linear continuous-time periodic systems is proposed in this paper. In the computation of theH∞norm, no Riccati differential equations are needed to solve and only eigenvalues of a monodromy matrix of the associated periodic Hamiltonian system will be evaluated. First, the monodromy matrix is expressed as the product of state transition matrices of the Hamiltonian system. Second, these state transition matrices, which have been proved to be symplectic matrices, are evaluated by a structure-preserving Magnus series method. Then, in order to preserve the standard symplectic form of the monodromy matrix, the structure-preserving matrices obtained by state transition matrices are employed to compute the monodromy matrix. At last, the effectiveness and the high accuracy of the proposed structure-preserving algorithm are demonstrated by numerical examples. [ABSTRACT FROM PUBLISHER]

A new reliable algorithm for computing -norm of linear time-varying periodic (LTP) systems in continuous-time domain is proposed in this article. The solving of -norm is firstly transformed into the solving of the periodic Lyapunov differential equation (PLDE). Then, the key point in this article is that a new method based on the interval mixed energy matrix and the interval transition matrix computed by the structure-preserving Magnus series method is proposed for solving the PLDE. With the solutions of PLDE, the -norm of LTP systems is evaluated by a simple first-order ordinary differential equation. Finally, the effectiveness and the high accuracy of the proposed algorithms are demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]