A new methodology to compute stabilizing control laws for continuous‐time LTV systems |
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| Authors: | Cristiano M Agulhari Germain Garcia Sophie Tarbouriech Pedro L D Peres |
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| Affiliation: | 1. Federal University of Technology of Paraná, Cornélio Procópio‐PR, Brazil;2. LAAS‐CNRS, University of Toulouse, Toulouse, France;3. School of Electric and Computer Engineering, University of Campinas, Campinas‐SP, Brazil |
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| Abstract: | 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. |
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| Keywords: | continuous‐time systems linear time‐varying systems Lyapunov stability stability analysis state‐feedback |
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