• Title/Summary/Keyword: monotone nondecreasing

### On Nonovershooting or Monotone Nondecreasing Step Response of Second-Order Systems

• Kwon, Byung-Moon;Lee, Myung-Eui;Kwon, Oh-Kyu
• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.283-288
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• 2002
• This paper has shown that the impulse and the unit step responses of 2nd-order systems can be computed by an analytic method. Three different 2nd-order systems are investigated: the prototype system, the system with one LHP(left half plane) real zero and the system with one RHP(right half plane) real zero. It has also shown that the effects of the LHP or the RHP zero are very serious when the zero is getting closer to the origin on the complex plane. Based on these analytic results, this paper has presented two sufficient and necessary conditions for 2nd-order linear SISO(single-input/single-output) stable systems to have the nonovershooting and the monotone nondecreasing step response, respectively. The latter condition can be extended to the sufficient conditions for the monotone nondecreasing step response of high-order systems.

### Sufficient and Necessary Condition for Monotone Nondecreasing Step Response of Second-Order System

• Kwon, Byung-Moon;Kwon, Oh-Kyu;Kim, Dae-Woo
• 제어로봇시스템학회:학술대회논문집
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• pp.96.1-96
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• 2001
• This paper is shown that the impulse and unit step response of second-order system can be computed by the analytic methods using Laplace transform. Also, the transient response specifications are explicitly formulated by the peak undershoot and maximum overshoot of the step response. Three different second-order systems are investigated: prototype system, system with LHP(left half plane) real zero, and system with RHP(right half plane) real zero. Based on these analytic results, this paper presents the sufficient and necessary conditions for the second-order linear SISO(single-input/single-output) stable system to have the nonovershooting or monotone nondecreasing step response.

### A Study on the Effects of Added Zeros to the System with a Monotone Nondecreasing Step Response

• Kwon, Byung-Moon;Lee, Hyun-Seok;Kwon, Oh-Kyu
• 제어로봇시스템학회:학술대회논문집
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• pp.44.4-44
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• 2002
• This paper investigates some conditions such that zeros are added to the system with a monotone nondecreasing step response in order to hold the monotonicity as before. Two conditions are presented for the cases that a real zero and complex conjugate zeros are added to the system satisfying the monotonicity condition, respectively. To exemplify the proposed results, some simple examples via computer simulation are shown in this paper. Proposed conditions can be easily used in the control system design since they are only formulated in terms of pole-zero configurations.

### Zeros and Step Response Characteristics in LTI SISO Systems with Complex Poles (복소극점을 갖는 선형시불변 단일입출력 시스템의 영점과 계단응답 특성)

• Lee, Sang-Yong
• Journal of Institute of Control, Robotics and Systems
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• v.16 no.4
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• pp.313-318
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• 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.

### Zeros and Step Response αlaracteristics in LTI SISO Systems (선형시불변 단일입출력 시스템의 영점과 계단응답 특성)

• Lee, Sang-Yong
• Journal of Institute of Control, Robotics and Systems
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• v.15 no.8
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• pp.804-811
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• 2009
• 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. As well known, if a system has a single unstable zero, it shows the step response with undershoot and, on the other hand, a stable zero slower than the dominant pole causes the system to have the step response with overshoot. Generally, in the case of a system with two unstable real zeros, it is known to have B type undershoot[7]. But there are many complex cases of the step response extrema corresponding to zeros location in third order systems. This paper investigates the whole cases depending on DC gains of the additive equivalence systems and they are to be classified by the region of zeros which are related to the shape of the step response. Moreover, monotone nondecreasing conditions are proposed in the case of complex conjugate zeros as well as the case of two stable zeros.

### HUGE CONTRACTION ON PARTIALLY ORDERED METRIC SPACES

• DESHPANDE, BHAVANA;HANDA, AMRISH;KOTHARI, CHETNA
• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.35-51
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• 2016
• We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X2 → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

### ON THE EXISTENCE OF A UNIQUE INVARIANT PROBABILITY FOR A CLASS OF MARKOV PROCESSES

• Lee, Oesook
• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.91-97
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• 1993
• In this article, we consider the case that S is a topologically complete subspace of $R^{k}$ , and that .GAMMA. is a set of monotone functions on S into S. It is obtained the sugficient condition for the existence of a unique invariant probability to which $P^{(n}$/(x,dy) converges exponentially fast in a metric stronger than the Kolmogorov's distance. This extends the earlier results of Bhattacharya and Lee (1988) who considered the case .GAMMA. a set of nondecreasing functions.tions.

### ASYMPTOTICS OF A CLASS OF ITERATED RANDOM MAPS

• Lee, ChanHo
• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.179-185
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• 1993
• In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

### ELLIPTIC SYSTEMS INVOLVING COMPETING INTERACTIONS WITH NONLINEAR DIFFUSIONS

• Ahn, In-Kyung
• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.123-132
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• 1995
• Our interest is to study the existence of positive solutions to the following elliptic system involving competing interaction $$(1) { -\partial(x,u,\upsilon)\Delta u = uf(x,u,v) { - \psi(x,u,\upsilon)\Delta \upsilon = \upsilon g(x,u,\upsilon) { \frac{\partial n}{\partial u} + ku = 0 on \partial\Omega { \frac{\partial n}{\partial\upsilon} + \sigma\upsilon = 0$$ in a bounded region $\Omega$ in $R^n$ with a smooth boundary, where the diffusion terms $\varphi, \psi$ are strictly positive nondecreasing function, and k, $\sigma$ are positive constants. Also we assume that the growth rates f, g are $C^1$ monotone functions. The variables u, $\upsilon$ may represent the population densities of the interacting species in problems from ecology, microbiology, immunology, etc.