• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.227-234
• /
• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• Communications of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.121-134
• /
• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.175-186
• /
• 2018

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.36 no.9
• /
• pp.670-677
• /
• 1987

The robustness and stability properties for a model reference adaptive control system with plant uncertainty are considered in this paper, using input-output stability theory. An error model for a typical adaptive control structure is extended to unmodelled dynamics in the plant model and then, the strictly positive real condition for global stability is examined. In general, since this condition can be easily violated due to unmodelled dynamics, a modified compensator which can be guaranteed Hev e SPR is introduced in the plant model and the effectiveness for the given structure is also given.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.39.2-39
• /
• 2001

This paper describes the design of an output-feedback controller based on an adaptive fuzzy observer for uncertain single-input single-output nonlinear dynamical systems. Especially, we have focused on the realization of minimal dynamic order of the adaptive fuzzy observer. For the purpose, we propose a new method in which no strictly positive real(SPR) condition is needed and combine dynamic rule activation scheme with on-line estimation of fuzzy parameters. By using proposed scheme, we can reduce computation time, storage space, and dynamic order of the adaptive fuzzy observer ...

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.24 no.6
• /
• pp.942-947
• /
• 1987

In this paper, we suggest a new adaptive control theory for discrete-time single-input single output systems based on the Lyapunov's stability theory by using the fact that the transfer function of the model is strictly positive real. And also, obervers are used in the structure of controller. The result of computer simulation shows that the proposed algorithm can be applied to both stable and unstable plants.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.103-108
• /
• 2016

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x_1+x_2)+f(x_2+x_3)+{\cdots}+f(x_n+x_1){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that $2{\leq}t$ < n.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.879-889
• /
• 2011

In this paper, we investigate the local asymptotic stability, the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation $x_{n+1}=\frac{a+bx_nx_{n-k}}{A+Bx_n+Cx_{n-k}}$, n = 0, 1,${\ldots}$, where the parameters a, b, A, B, C and the initial conditions $x_{-k}$, ${\ldots}$, $x_{-1}$, $x_0$ are positive real numbers.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.179-186
• /
• 2010

This paper concerns the propagation phenomenon of weighted shifts. We here establish the existence of positive real numbers b and c (1 < b < c) such that the recursive weighted shift $W_{1,(1,\sqrt{b}\sqrt{c})$^ is quadratically but not cubically hyponormal.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.211-218
• /
• 2003

Let H be a Hilbert space, X be a real Banach space, A : H \longrightarrow X be an operator with D(A) dense in H, G： H \longrightarrow H be positive definite, $\chi$ $\in$ D(A) and b $\in$ H. Consider the quadratic programming problem: QP： Minimize $\frac{1}{2}$〈p, $\chi$〉 + 〈$\chi$, G$\chi$〉 subject to A$\chi$= b In this paper, we obtain an explicit solution to the above problem using generalized inverses.