A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence

• Published in: Systems & control letters Vol. 54; no. 11; pp. 1131 - 1134
• Main Authors: de Oliveira, M.C., Geromel, J.C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2005; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; formula omitted; Miscellaneous; Modelling and identification; Robust stability; Parameter dependent Lyapunov function; Linear matrix inequalities; Control program; Linear condition; Robust control; Linear time invariant system; Uncertain system; Discrete time; Linear matrix inequality; Linear stability; Feasibility; Lyapunov function
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2005.02.015

In previous works we have proposed a robust stability condition for linear time-invariant discrete-time systems which makes use of a Lyapunov function with linear dependence on the uncertain parameters. This condition is expressed as a set of linear matrix inequalities (LMI) where an additional variable is kept common to all LMI. These features have enabled the development of successful robust filtering and control algorithms. In this short note we investigate possible extensions of this stability condition to handle Lyapunov functions with arbitrary parameter dependence while keeping a variable common to all LMI. By showing that feasibility of the original condition is indeed necessary for the existence of a family of robust stability conditions where the Lyapunov function can have arbitrary dependence on the uncertain parameters, we conclude that no such extensions are possible.