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A Continuation Method for computation of H∞ gains of Linear Continuous-Time Periodic Systems

A continuation method is applied to compute the H∞ gain of a periodic linear system. The H∞ gain of a periodic linear system can be equivalently found by solving a Periodic Differential Riccati Equation (PDRE) for an increasing sequence of gain candidates until no solution exists. Solving the PDRE can be cumbersome. However, for a null gain candidate, the PDRE is a Periodic Differential Lyapunov Equation (PDLE) that can be solved efficiently. Similarly, for a small increase in the gain candidate, the solution can be approximated by solving another PDLE. We describe an application of the continuation method where the corrector uses a Boundary Value Problem solver. Therefore, using a continuation method can be promising for such a problem. The gain candidate is increased until no solution to the PDRE exists. Compared to Hamiltonian based approaches, our approach suffers less from ill-conditioned differential equations for systems where the periodicity is long compared to the dynamic of the system of interest.