Fixed-structure LPV discrete-time controller design with induced l₂-norm and H2 performance

ABSTRACT

A new method for the design of fixed-structure dynamic output-feedback linear parameter-varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, ${\mathcal{H}}_2$ and induced l₂-norm performance of a given LPV system are represented through a set of linear matrix inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.

Keywords:

• Linear parameter-varying
• fixed-structure controller design
• parameter-dependent Lyapunov function
• induced l₂-norm performance
• ${\mathcal{H}}_2$ performance
• scheduling parameter uncertainty

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work was financially supported by the Swiss National Science Foundation [grant number 200021-121749].