3 research outputs found
Lagrange Stabilization of Pendulum-like Systems: A Pseudo H-infinity Control Approach
This paper studies the Lagrange stabilization of a class of nonlinear systems
whose linear part has a singular system matrix and which have multiple periodic
(in state) nonlinearities. Both state and output feedback Lagrange
stabilization problems are considered. The paper develops a pseudo H-infinity
control theory to solve these stabilization problems. In a similar fashion to
the Strict Bounded Real Lemma in classic H-infinity control theory, a Pseudo
Strict Bounded Real Lemma is established for systems with a single unstable
pole. Sufficient conditions for the synthesis of state feedback and output
feedback controllers are given to ensure that the closed-loop system is pseudo
strict bounded real. The pseudo H-infinity control approach is applied to solve
state feedback and output feedback Lagrange stabilization problems for
nonlinear systems with multiple nonlinearities. An example is given to
illustrate the proposed method