An LMI-based algorithm for static output-feedback stabilization of continuous-time positive polytopic linear systems

Author(s)

Lemaire, Alvaro A. ; Spagolla, Amanda ; Morais, Cecilia F. ; Oliveira, Ricardo C. L. F. ; Peres, Pedro L. D.

• Document type: Journal article
• Source: IFAC PAPERSONLINE; v. 53, n. 2, p. 6-pg., 2020-01-01.

Abstract

This paper presents a new technique to design static output-feedback controllers for continuous-time positive uncertain linear systems. The design is performed through an iterative algorithm based on parameter-dependent linear matrix inequality conditions, solved by means of relaxations, with local convergence guaranteed. A qualified feasible solution provides a stabilizing output-feedback controller that also assures the positivity of the closed-loop system. The main advantage of the proposed methodology is that the control gain is handled directly as an optimization variable, that is, no change of variables is needed to recover the gain and no particular structure (e.g., diagonal) is imposed on the Lyapunov or slack variable matrix to guarantee closed-loop positivity. This particular feature also facilitates the design of decentralized or element-wise bounded gains, as illustrated by numerical experiments. Copyright (C) 2020 The Authors. (AU)

• FAPESP's process: 17/18785-5 - Parameter-Dependent Linear Matrix Inequalities Applied to Stability Analysis and Synthesis of Controllers and Filters for Uncertain Dynamic Systems
• Grantee: Pedro Luis Dias Peres
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/09363-5 - Control of uncertain positive linear systems by means of linear matrix inequalities
• Grantee: Amanda Spagolla
• Support Opportunities: Scholarships in Brazil - Doctorate