Seok Young Lee, Won Il Lee, PooGyeon Park
International Journal of Robust and Nonlinear Control
AbstractThis paper proposes a novel summation inequality, say a polynomials-based summation inequality, which contains well-known summation inequalities as special cases. By specially choosing slack matrices, polynomial functions, and an arbitrary vector, it reduces to Moon's inequality, a discrete-time counterpart of Wirtinger-based integral inequality, auxiliary function-based summation inequalities employing the same-order orthogonal polynomial functions. Thus, the proposed summation inequality is more general than other summation inequalities. Additionally, this paper derives the polynomials-based summation inequality employing first-order and second-order orthogonal polynomial functions, which contributes to obtaining improved stability criteria for discrete-time systems with time-varying delays.
Signal Processing and Control Laboratory has been organized since 1996. Our current research interests include convex optimization theories and their applications in control, estimation and signal processing.