Efficient computation of the L-infinity norm of descriptor systems

Abstract

Many applications from industry and technology use models formulated by systems of differential equations. Often, some equations describe additional algebraic constraints. Such systems, referred to as descriptor systems (or singular systems), naturally arise, e.g., in electrical circuit simulation, in multibody dynamics with constraints, or by semidiscretization of certain partial differential equations. A very important characteristic value for a descriptor system is the L∞-norm of its corresponding transfer function. The computation of this norm is essential in robust control, model order reduction, and other applications. The paper summarizes efficient and reliable algorithms for finding L∞-norm, for continuous- and discrete-time descriptor systems, which exploit the underlying Hamiltonian or symplectic structure, respectively. An improved solver has been developed and will be made available in the SLICOT Library. Numerical results and comparisons illustrate the good performance and effectiveness of this solver.