Analysis and design of quadratically bounded QPV control systems

© 2019. ElsevierA 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.Peer ReviewedPostprint (author's final draft

D-stable controller design for Lipschitz NLPV system

This paper addresses the design of a state-feedback controller for a class of nonlinear parameter varying (NLPV) systems in which the nonlinearity can be expressed as a parameter-varying Lipschitz term. The controller is designed to satisfy a D-stability specification, which is akin to imposing constraints on the closed-loop pole location in the case of LTI and LPV systems. The design conditions, obtained using a quadratic Lyapunov function, are eventually expressed in terms of linear matrix inequalities (LMIs), which can be solved efficiently using available solvers. The effectiveness of the proposed method is demonstrated by means of a numerical example.Postprint (author's final draft

Nonlinear parameter‐varying state‐feedback design for a gyroscope using virtual control contraction metrics

In this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter-varying approach to design a state-feedback controller for a control moment gyroscope (CMG) to track a user-defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter-varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and (Formula presented.) -gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully- and under-actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods