L _∞ and L_2 semi-global stabilisation of continuous-time periodic linear systems with bounded controls

摘要

This article is concerned with L _∞ and L_2 semi-global stabilisation of continuous-time periodic linear systems with bounded controls. Two problems, namely L_∞ semi-global stabilisation with controls having bounded magnitude and L_2 semi-global stabilisation with controls having bounded energy, are solved based on solutions to a class of periodic Lyapunov differential equations (PLDEs) resulting from the problem of minimal energy control with guaranteed convergence rate. Under the assumption that the open-loop system is (asymptotically) null controllable with constrained controls, periodic feedback are established to solve the concerned problems. The proposed PLDE-based approaches possess the advantage that the resulting controllers are easy to implement since the designers need only to solve a linear differential equation. A numerical example is worked out to illustrate the effectiveness of the proposed approach.