• Journal of Institute of Control, Robotics and Systems
• /
• v.16 no.4
• /
• pp.313-318
• /
• 2010

This paper deals with the relationship between zeros and step response of the second and third order LTI (Linear Time Invariant) SISO (Single-Input and Single-Output) systems with complex poles. Although it has been known that the maximum number of local extrema is less than the number of zeros in the system with only real poles[8], some cases with complex poles are shown in this paper to have many local extrema. This paper proposes monotone nondecreasing conditions and describes the relationship between the transient response and the number of local extrema in step response with each region of zeros.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.507-513
• /
• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• Kyungpook Mathematical Journal
• /
• v.55 no.3
• /
• pp.641-652
• /
• 2015

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain $D{\subseteq}{\mathbb{C}}$ and n, k be two positive integers such that $n{\geq}k+1$, and let a, b be two finite complex constants such that $a{\neq}0$. Suppose that (1) $f+a(f^{(k)})^n$ and $g+a(g^{(k)})^n$ share b in D for every pair of functions f, $g{\in}F$; (2) All zeros of f have multiplicity at least k + 2 and all poles of f have multiplicity at least 2 for each $f{\in}F$ in D; (3) Zeros of $f^{(k)}(z)$ are not the b points of f(z) for each $f{\in}F$ in D. Then F is normal in D. And some examples are provided to show the result is sharp.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.22 no.1
• /
• pp.101-121
• /
• 1997

Consider a Jackson type closed queueing network in which each queue has a single exponential server. Assume that N customers are moving among .kappa. queues. We propose a candidata procedure which yields a lower bound of the network throughput which is sharper than those which are currently available : Let (.rho.$_{1}$, ... .rho.$_{\kappa}$) be the loading vector, let x be a real number with 0 .leq. x .leq. N, and let y(x) denote that y is a function of x and be the unique positive solution of the equation. .sum.$_{i = 1}$$^{\kappa}$y(x) .rho.$_{i}$ (N - y(x) x $p_{i}$ ) = 1 Whitt [17] has shown that y(N) is a lower bound for the throughput. In this paper, we present evidence that y(N -1) is also a lower bound. In dosing so, we are led to formulate a rather general conjecture on 'quot;Migrating Critical Points'quot; (MCP). The .MCP. conjecture asserts that zeros of successive derivatives of certain rational functions migrate at an accelerating rate. We provide a proof of MCP in the polynomial case and some other special cases, including that in which the rational function has exactly two real poles and fewer than three real zeros.tion has exactly two real poles and fewer than three real zeros.

• International journal of advanced smart convergence
• /
• v.6 no.4
• /
• pp.33-40
• /
• 2017

In this paper, complex quadruplet zeros of microwave filter systems are investigated. For the cascaded systems the chain matrices are most conveniently used to derive the voltage transfer function of Laplace transform with cascaded two-port subsystems. The convenient relations of transfer function and chain matrix are used in order to find the transmission zeros. Starting from a ladder network, we introduced a crossed-coupled lumped element, in order to show the improved response of bandpass filter. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we found the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. When the two pairs of double are on the zeros -axis, with the perturbed values of element, we learned that the transition band of lowpass filter is improved. By solving the characteristic equation of cascaded transfer function, we can obtain the zeros of the cross-coupled filter system, as a result of perturbed values on lumped element.

• Proceedings of the IEEK Conference
• /
• 2000.07b
• /
• pp.681-684
• /
• 2000

Gradient-type algorithms for adaptive IIR notch filters are very attractive in terms of both performances and computational requirements. Generally, it is quite difficult to assess their performances analytically. There have been several trials to analyze such adaptive algorithms as the sign and the plain gradient algorithms for some types of adaptive IIR notch filters, but many of them still remain unexplored. Furthermore, analysis techniques used in those trials can not be directly applied to different types of adaptive IIR notch filters. This paper presents a detailed performance analysis of the sign algorithm for a well-known adaptive IIR notch filter with constrained poles and zeros, which can not be done by just applying the related existing analysis techniques, and therefore has not been attempted yet. The steady-state estimation error and mean square error (MSE) of the algorithm are derived in closed forms. Stability bounds of the algorithm are also assessed. extensive simulations are conducted to support the analytical findings.

• Smart Structures and Systems
• /
• v.14 no.6
• /
• pp.1081-1103
• /
• 2014

Real-time hybrid simulation (RTHS) has emerged as an important tool for testing large and complex structures with a focus on rate-dependent specimen behavior. Due to the real-time constraints, accurate dynamic control of servo-hydraulic actuators is required. These actuators are necessary to realize the desired displacements of the specimen, however they introduce unwanted dynamics into the RTHS loop. Model-based actuator control strategies are based on linearized models of the servo-hydraulic system, where the controller is taken as the model inverse to effectively cancel out the servo-hydraulic dynamics (i.e., model-based feedforward control). An accurate model of a servo-hydraulic system generally contains more poles than zeros, leading to an improper inverse (i.e., more zeros than poles). Rather than introduce additional poles to create a proper inverse controller, the higher order derivatives necessary for implementing the improper inverse can be calculated from available information. The backward-difference method is proposed as an alternative to discretize an improper continuous time model for use as a feedforward controller in RTHS. This method is flexible in that derivatives of any order can be explicitly calculated such that controllers can be developed for models of any order. Using model-based feedforward control with the backward-difference method, accurate actuator control and stable RTHS are demonstrated using a nine-story steel building model implemented with an MR damper.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.3
• /
• pp.621-633
• /
• 2024

Let R_n be the space of rational functions with prescribed poles. If r ∈ R_n, does not vanish in |z| < k, then for k = 1 $${\mid}r^{\prime}(z){\mid}{\leq}{\frac{{\mid}B^{\prime}(z){\mid}}{2}}\sup_{z{\in}T}{\mid}r(z){\mid}$$, where B(z) is the Blaschke product. In this paper, we consider a more general class of rational functions rof ∈ R_m*n, defined by (rof)(z) = r(f(z)), where f(z) is a polynomial of degree m^* and prove a more general result of the above inequality for k > 1. We also prove that $$\sup_{z{\in}T}\left[\left|{\frac{r^{*\prime}(f(z)}{B^{\prime}(z)}}\right|+\left|{\frac{r^{\prime}(f(z))}{B^{\prime}(z)}}\right|\right]=\sup_{z{\in}T}\left|{\frac{(rof)(z)}{f^{\prime}(z)}}\right|$$, and as a consequence of this result, we present a generalization of a theorem of O'Hara and Rodriguez for self-inverse polynomials. Finally, we establish a similar result when supremum is replaced by infimum for a rational function which has all its zeros in the unit circle.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.21 no.11
• /
• pp.1259-1268
• /
• 2010

In this paper, we presented a new LC prototype synthesis method for the multi-band filter. For synthesis a multi-band filter with the required frequency response, we proposed the diagram of poles and zeros, also, we proposed the optimization process for finding the combination of optimized poles and zeros. From the transfer and reflection functions calculated from poles and zeros, we performed the quasi-elliptic LC prototype synthesis of multi-band filter. Using the proposed LC prototype synthesis method of multi-band filter, dual-band filter operating at GSM(880~960 MHz) and ISM(2,400~2,500 MHz) and triple-band filter operating at GSM(880~960 MHz) and ISM(2,400~2,500, 5,725~5,850 MHz) were designed and fabricated.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.151.1-151
• /
• 2001

This paper establishes some integral equalities formulated by zeros located in the convergence region of Laplace transformable function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the function, and those can be applied to understanding of the fundamental limitations of the control system represented by the transfer function, which has been Laplace transform. In the unity-feedback control scheme, another integral equality is also derived on the output response of the system with open-loop poles and zeros located in the convergence region.