Computing stabilising output-feedback gains for continuous-time linear time-varying systems through discrete-time periodic models

Abstract

A methodology for the synthesis of time-varying static output-feedback gains, capable of stabilising continuous-time linear time-varying systems, is proposed in this paper. The method is based on the computation of output-feedback gains that stabilise a family of periodic discrete-time subsystems, related to the original model, followed by a transformation that yields the desired stabilising gains for the continuous-time system. Based on such strategy, three different approaches to compute stabilising periodic discrete-time gains, as well as the necessary transformations to generate the continuous-time output-feedback gains, are proposed. Numerical examples are presented in order to compare and analyze the efficiency of the proposed approaches.

Keywords:

• Output feedback
• linear systems
• time-varying systems
• continuous-time systems
• Lyapunov stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The stability analysis can be performed by computing the eigenvalues of the monodromy matrix $\mathrm{\Phi }(N,0)$.