H∞ control for linear descriptor systems with non-differentiable delays in both state and observation. (3rd August 2021)

• Record Type: Journal Article
• Authors: Niamsup, P.; Phat, V. N.
• Is Part Of: Optimization. Volume 70:Number 8(2021)
• Page Start: 1809
• Page End: 1823
• Publication Date: 2021-08-03
• Subjects: H∞ control -- descriptor systems -- stabilization -- non-differentiable delay -- linear matrix inequalities; 93D05 -- 49N05 -- 34D15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1753740
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: This paper deals with the problem of H ∞ control for linear descriptor systems with time-variable delay. The delay function, which is non-differentiable, appears in both the state and observation. For stability, appropriate Lyapunov–Krasovskii functionals are constructed to eliminate the derivative calculating of the delay function and utilize smaller number of linear matrix inequality decision variables. The proposed functionals are employed to derive new delay-dependent sufficient conditions for admissibility of the unforced descriptor closed-loop system. For H ∞ control, we design state feedback controllers which make the descriptor closed-loop system admissible with a maximum H ∞ disturbance attenuation level. A numerical example with simulation is given to illustrate the effectiveness of the proposed method.