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摘要
Purpose - This purpose of this paper is to discuss a linear fractional representation (LFR) of parameter-dependent systems which are linear in the parameters but uncertain, being eventually time-varying real-rational nonlinear parameterizations, and dynamics with constant point delays.
Design/methodology/approach - The formulation is made in terms of Lyapunov's second method whereby the Lyapunov function candidate is confirmed to be a Lyapunov function by testing a finite number of linear-matrix inequalities when the uncertain parameter vector, which might be time-varying, lies within a known polytope which characterizes the uncertainties. The tests are performed only on the set of vertices associated with polytopes.
Findings - Sufficient conditions for global asymptotic stability are obtained. Conditions constraining the system to be slowly time-varying around a stable nominal parameterization are not imposed in order to guarantee the stability.
Research limitations/implications - The formulation is applied to a class of systems whose uncertainties might be parameterized through time-varying real-rational nonlinear parameterizations and which include point-delayed dynamics with constant delays. However, such a class includes certain classes of neural networks with delays, systems with switched parameterizations and systems whose uncertain dynamics evolve arbitrarily in regions defined by known polytopes.
Practical implications - The stability tests are less involved than usual for time-varying systems since only a finite number of them is necessary to investigate the stability.
Originality/value - LFR descriptions of linear time-varying systems are extended to a wide class of systems with constant point delays. Also, the real-rational nonlinear parameterizations of the uncertainties are admitted in both the delay-free and delayed dynamics.
- 出版日期2007
