Jeong Wan Ko

Reciprocally convex approach to stability of systems with time-varying delays

Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by Moon, Park, Kwon, and Lee (2001), plays a key role in guiding various delay-dependent criteria for delayed systems, the Jensen inequality has become an alternative as a way of reducing the number of decision variables. It directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities, resulting in a linear combination of positive functions weighted by the inverses of convex parameters. This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to those based on the Jensen inequality lemma.

Mean-Square Deviation Analysis of Affine Projection Algorithm

This paper presents an improved mean-square deviation (MSD) analysis of the standard affine projection algorithm (APA) based on two distinctive features. First, the propagation model of the error covariance includes the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs; such a cross-correlation has merely been considered previously. Second, the analysis based on n most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where n denotes the tap-length of the filter. Simulation results are in better agreement with the proposed theoretical results, than the previous theoretical ones, over a wide range of parameters such as tap-length, projection order, and step-size.

Technical communique: Stabilization for Takagi-Sugeno fuzzy systems based on partitioning the range of fuzzy weights

In this note, the state-feedback stabilization for continuous-time Takagi-Sugeno (T-S) fuzzy systems is addressed, where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are possibly bounded by some parameters. By utilizing the matrix elimination lemma and introducing a polyhedral partition to the range of the fuzzy weights, the quadratically parameterized condition is transformed to being piecewise linear in both the fuzzy weights and their derivatives. Then, a switching control based on the partition is considered, by utilizing the extreme points in each partition to address the constraints of the fuzzy weights and their derivatives. The simulation shows that finer subdivision in the partition leads to better stability and stabilization margins.

Improved global stability conditions of the tuning parameter in FAST TCP

In this letter, we present a correction of the theorem for the global stability of FAST TCP developed by Koo et al. in 2008. Furthermore, an analysis is carried out to determine an improved parameter condition for global stability than the existing conditions in the literature. The parameter condition is verified by the ns-2 simulation.

Stabilization of the asymmetric network control system using a deterministic switching system approach

We propose an Internet-based network control structure, the asymmetric network control system. By using the system characteristics and modeling it as a deterministic switching system, we formulate the stabilization problem of the system in terms of linear matrix inequalities. In the formulation, two cases when using piecewise Lyapunov functions and a common Lyapunov function are both considered.

Reciprocally Convex Approach for the Stability of Networked Control Systems

This chapter deals with the problem of stability analysis for networked control systems via the time-delayed system approach. The network-induced delays are modeled as two additive time-varying delays in the closed-loop system. To check the stability of such particular featured systems, an appropriate Lyapunov–Krasovskii functional is proposed and the Jensen inequality lemma is applied to the integral terms that are derived from the derivative of the Lyapunov–Krasovskii functional. Here, the cascaded structure of the delays in the system enables one to partition the domain of the integral terms into three parts, which produces a linear combination of positive functions weighted by inverses of convex parameters. This is handled efficiently by the authors’ lower bounds lemma that handles the so-called reciprocally convex combination.

State-Feedback Switching Control for Discrete-Time Takagi-Sugeno Fuzzy Systems Based on Partitioning The Range of Fuzzy Weights

In this paper, we propose an efficient relaxation method of the parameterized linear matrix inequalities (PLMIs) in the framework of the state-feedback stabilization problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems. The matrix elimination method plays a key role in deriving the criterion, which reduces the order of the fuzzy weights by eliminating the quadratic fuzzy weights in the original PLMIs and then transformed to a more tractable one. A partition on the range of the fuzzy weights is introduced, through which a linearly weight-dependent condition can be developed by fixing some decision variables piecewisely. By utilizing the extreme points of each partition, the negativity of the condition can be guaranteed and the corresponding controller is represented in the form of a switching control law based on the partition. Some example shows that finer subdivision in the partition leads to a better performance behavior.