Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

Abstract

This paper presents novel linear matrix inequalities (LMI)-based conditions to address the coprime factorization problem for polytopic linear parametervarying (LPV) systems in both the continuous-and discrete-time cases. The proposed conditions rely on the use of homogeneous polynomial parameterdependent (HPPD) matrix solutions of arbitrary degree g, which are used to obtain coprime factorization descriptions subject to time-varying parameters defined inside a polytopic structure with known vertices. For a given degree g, synthesis of right and left coprime factorizations in terms of two special state-feedback and filtering problems under quadratic H 2 performance are provided. Existence conditions are given from linear matrix inequalities relaxations based on an extension of Pólya's theorem and the HPPD approach. The effectiveness of the proposed conditions is evaluated by means of numerical examples.

Data‐driven safe gain‐scheduling control

“…This section formulates problems of safe control design for polytopic LPV systems with both polyhedral and ellipsoidal safe sets. Consider the discrete polytopic LPV system given by [39][40][41]…”

“…Consider the discrete polytopic LPV system given by [39–41] $$$$ x\left(t+1\right)=A\left(w(t)\right)x(t)+ Bu(t), $$$$ where $$$ x(t)\in X $$$ is the system's state and $$$ u(t)\in \mathcal{U} $$$ is the control input with $$$ X $$$ and $$$ \mathcal{U} $$$ as constrained sets (e.g., ellipsoidal or polyhedral) containing the origin in their interiors. Moreover, $$$ B\in {R}^{n\times m} $$$ is the input dynamic and is assumed fixed.…”