A positive definiteness preserving discretization method for Lyapunov differential equations

Periodic Lyapunov differential equations can be used to formulate robust optimal periodic control problems for nonlinear systems. Typically, the added Lyapunov states are discretized in the same manner as the original states. This straightforward technique fails to guarantee conservation of positive-semidefiniteness of the Lyapunov matrix under discretization. This paper describes a discretization method, coined PDPLD, that does come with such a guarantee. The applicability is demonstrated at hand of a tutorial example, and is specifically suited for direct collocation methods.status: publishe