A new methodology to compute stabilizing control laws for continuous‐time LTV systems. (24th April 2018)

• Record Type: Journal Article
• Authors: Agulhari, Cristiano M.; Garcia, Germain; Tarbouriech, Sophie; Peres, Pedro L. D.
• Is Part Of: International journal of robust and nonlinear control. Volume 28:Number 13(2018)
• Page Start: 4045
• Page End: 4057
• Publication Date: 2018-04-24
• Subjects: continuous‐time systems -- linear time‐varying systems -- Lyapunov stability -- stability analysis -- state‐feedback; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4120
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper is devoted to the problem of computing control laws for the stabilization of continuous‐time linear time‐varying systems. First, a necessary and sufficient condition to assess the stability of a linear time‐varying system based on the norm of the transition matrix computed over a sequence of successive finite‐time intervals is proposed. A link with a stability condition for an equivalent discrete‐time model is also established. Then, 3 approaches for the computation of stabilizing state‐feedback gains are proposed: a continuous‐time technique, ie, directly derived from the stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete‐time equivalent model along with a transformation to generate the desired continuous‐time gain; and the computation of stabilizing gains for a set of periodic discrete‐time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete‐time systems, an algorithm for the computation of a stabilizing state‐feedback continuous‐time gain is proposed. A numerical example illustrates the validity of the technique.