Jung Hoon Kim

This paper develops a new discretization method with piecewise linear approximation for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> optimal controller synthesis problem of sampled-data systems, which is the problem of minimizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_

This paper is concerned with the delay-dependent stability for the linear systems with a time-varying delay. To get a result in the form of LMI from a Lyapunov–Krasovskii functional, an integral inequality is necessary and Jensen inequality has been a most powerful inequality in the last few years. Recently, based on Wirtinger inequality, an improved integral inequality, encompassing Jensen inequality, was proposed and its application to the stability showed a quite improvement. In this paper, w

This study deals with the L 1 analysis of stable finite‐dimensional linear time‐invariant (LTI) systems, by which the authors mean the computation of the L ∞ ‐induced norm of these systems. To compute this norm, they need to integrate the absolute value of the impulse response of the given system, which corresponds to the kernel function in the convolution formula for the input/output relation. However, it is very difficult to compute this integral exactly or even approximately with an explicit

The aim of this paper is to construct a theoretical framework for stability analysis relevant to standing balance of humanoids on top of the linear inverted pendulum model, in which their dynamics between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. Based on the well-known sufficient condition that the contact between the ground and the support leg is stable if the corresponding ZMP is always inside the supporting region, this paper aims at characterizing three types o

This paper is concerned with linear time-invariant (LTI) sampled-data systems (by which we mean sampled-data systems with LTI generalised plants and LTI controllers) and studies their H 2 norms from the viewpoint of impulse responses and generalised H 2 norms from the viewpoint of the induced norms from L 2 to L ∞. A new definition of the H 2 norm of LTI sampled-data systems is first introduced through a sort of intermediate standpoint of those for the existing two definitions. We then establish

This paper gives two methods for the L1 analysis of sampled-data systems, by which we mean computing the L∞-induced norm of sampled-data systems. This is achieved by developing what we call the kernel approximation approach in the setting of sampled-data systems. We first consider the lifting treatment of sampled-data systems and give an operator theoretic representation of their input/output relation. We further apply the fast-lifting technique by which the sampling interval [0, h) is divided i

In this paper, we build a generalized two-sector Kaleckian growth model and explore the dynamics towards long-run positions. The model incorporates conflicting claims of labour and firms over income distribution and endogenous labour-saving technical progress. Adopting a stock-flow consistent framework, our simulation experiments yield the following results. First, the ‘paradox of thrift’ and the ‘paradox of costs’ hold, meaning that lower saving rates generate higher growth rates while higher r

Abstract This article provides a new framework for the so‐called L 1 optimal control problem of sampled‐data systems, that is, the synthesis problem of a discrete‐time optimal controller minimizing the continuous‐time L ∞ ‐induced norm of the closed‐loop system for a given continuous‐time plant. The main idea is to develop the approximation method called the piecewise linear kernel approximation (PLKA) method, by which the kernel function of the input operator together with the hold function of

This note studies the spectral properties of monodromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The note is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy op

This paper is concerned with performance analysis of proportional-derivative/proportional-integral-derivative (PD/PID) controller for bounded persistent disturbances in a robotic manipulator. Even though the notion of input-to-state stability (ISS) has been widely used to deal with the effect of disturbances in control of a robotic manipulator, the corresponding studies cannot be directly applied to the treatment of persistent disturbances occurred in robotic manipulators. This is because the co