A Riccati transformation method for solving linear BVPs. I: theoretical aspects
SIAM Journal on Numerical Analysis
Numerical integration of the differential Riccati equation and some related issues
SIAM Journal on Numerical Analysis
A lifting technique for linear periodic systems with applications to sampled-data control
Systems & Control Letters
Linear robust control
H∞ sampled-data synthesis and related numerical issues
Automatica (Journal of IFAC)
A Natural Approach to the Numerical Integration of Riccati Differential Equations
SIAM Journal on Numerical Analysis
Technical Communique: Approximation of frequency response for sampled-data control systems
Automatica (Journal of IFAC)
Implementing the Hamiltonian test for the H∞ norm in linear continuous-time periodic systems
Automatica (Journal of IFAC)
Robust dynamical compensator design for discrete-time linear periodic systems
Journal of Global Optimization
| Hi-index | 22.14 |
A method to compute the L"2 gain is developed for the class of linear periodic continuous-time systems that admit a finite-dimensional state-space realisation. A bisection search for the smallest upper bound on the gain is employed, where at each step an equivalent discrete-time problem is considered via the well-known technique of time-domain lifting. The equivalent problem involves testing a bound on the gain of a linear shift-invariant discrete-time system, with the same state dimension as the periodic continuous-time system. It is shown that a state-space realisation of the discrete-time system can be constructed from point solutions to a linear differential equation and two differential Riccati equations, all subject to only single-point boundary conditions. These are well behaved over the corresponding one period intervals of integration, and as such, the required point solutions can be computed via standard methods for ordinary differential equations. A numerical example is presented and comparisons made with alternative techniques.