Abstract
This paper investigates the problem of a state bounding estimation for a linear continuous-time singular system with time-varying delay. By employing the maximal Lyapunov–Krasovskii functional and applying the new free-matrix-based integral inequality, some proper conditions are derived in terms of LMIs and a bounding estimation lemma and set are obtained for the studied singular system.
Highlights
During the past years, state bounding estimation has been widely applied in control systems with actuator saturation, peak-to-peak gain minimization, and parameter estimation
By applying the S-procedure, an ellipsoid reachable set bounding was derived for linear systems without time delays in [19]
By employing the maximal Lyapunov–Krasovskii functional and applying the new free-matrix-based integral inequality, some proper conditions are derived in terms of LMIs and a new bounding estimation lemma and set are obtained for the studied singular system
Summary
State bounding estimation has been widely applied in control systems with actuator saturation, peak-to-peak gain minimization, and parameter estimation (see [1,2,3,4,5]). By applying the S-procedure, an ellipsoid reachable set bounding was derived for linear systems without time delays in [19]. In [7], a delay-dependent criterion for an ellipsoid reachable bounding set was derived by Fridman and Shaked, applying a Lyapunov–Krasovskii functional.
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