Analysis and design of quadratically bounded QPV control systems

Abstract

A nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.