Parameter-Dependent Lyapunov Functions for Exact Stability Analysis of Single-Parameter Dependent LTI Systems
نویسندگان
چکیده
In this paper, we propose a class of parameterdependent Lyapunov functions which can be used to assess the stability properties of linear, time-invariant, single-parameter dependent (LTIPD) systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem.
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