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• # 2015 open lab program

Welcome to our homepage!
• # 2015 SPaC homecoming

Welcome to Signal Processing and Control laboratory!!

#### Robust Control

Robust control is a branch of control theory whose approach to controller design explicitly deals with uncertainty.

#### Time Delay System

Systems with time-delays are called time-delay systems. Controls of time delay systems are more complicated compared to ordinary systems.

An adaptive filter is a system with a linear filter that has a transfer function controlled by variable parameters and a means to adjust those parameters according to an optimization algorithm.

#### Image Processing

Image processing is processing of images using mathematical operations by using any form of signal processing for which the input is an image.
• ## Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

Seok Young Lee, Won Il Lee, PooGyeon Park

Journal of the Franklin Institute

Abstract Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays.
• ## Delays-Dependent region partitioning approach for stability criterion of linear systems with multiple time-varying delays

Kab Seok Ko, Won Il Lee, PooGyeon Park, Dan Keun Sung

Automatica

Abstract This paper considers a delay-dependent stability criterion for linear systems with multiple time-varying delays. To exploit all possible information for the relationships among the marginally delayed states (x(t−τiM)x(t−τi+1M)), the exactly delayed states (x(t−τi(t)),x(t−τi+1(t))), and the current state x(t) for each pair (i,i+1) of time-varying delays, a delays-dependent region partitioning approach in double integral terms is proposed. By applying the Wirtinger-based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning, a stability criterion is derived in terms of linear matrix inequalities. Numerical examples show that the resulting criterion outperforms the existing one in literature.
• ## \mathcal {H} _\infty  H∞ state-feedback control for continuous-time Markovian jump fuzzy systems using a fuzzy weighting-dependent Lyapunov function

Nam Kyu Kwon, In Seok Park, PooGyeon Park

Nonlinear Dynamics

Abstract This paper proposes a method for designing an HH∞ state-feedback fuzzy controller for continuous-time Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates. To find HH∞ control for level γγ, the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) for the MJFSs based on a fuzzy weighting-dependent Lyapunov function. Besides, to derive less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Finally, three examples are provided to verify the effectiveness of the proposed method.