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This paper addresses the vibration reduction and disturbance attenuation problems of a flexible arm, which is modelled as a fourth-order partial differential equation. The main control objectives lie in reducing the influence of the disturbance, steering the flexible arm to the desired angular position and suppressing the vibration, simultaneously. To achieve the objectives, firstly, two different disturbance observers are designed. Secondly, we construct boundary controllers based on the two designed disturbance observers and boundary measurable signals. Then, with the two disturbance observers, the boundary disturbance compensation is achieved, and with the designed boundary controllers, the uniform boundedness of the flexible arm is guaranteed. Moreover, the well-posedness of the closed-loop system under the designed boundary controllers is discussed by means of the operator semigroup theory. Finally, the effectiveness and advantages of the proposed controllers are demonstrated through simulations and physical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a diffusive prey-predator model with hunting cooperation and prey-taxis is proposed and investigated. First, we prove the uniform boundedness and global existence of time-varying solutions to the model. Then the stability and prey-taxis-driven instability of positive equilibrium are discussed through linearization analysis. It is found that negative prey-taxis may change the spatial stability of the positive equilibrium, implying formation of Turing pattern. Next, we discuss the existence and stability of the spatial pattern by choose the prey-tactic sensitivity coefficient as bifurcation parameter. Finally, some numerical simulations are performed to visualize the impact of prey-taxis on the complex spatial pattern formation. [ABSTRACT FROM AUTHOR]

According to a very recent paper [5], the positive solution of the two-dimensional Hénon equation will concentrate on finite points when $ p\to \infty $. In this short note, we prove the uniform boundedness of the solution and then obtain a formula to specify the location of the concentration points by a Kirchoff-Routh type function. [ABSTRACT FROM AUTHOR]

We analyse a reaction–diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. A generalized model is formulated on a one dimensional bounded domain with feed terms at one end of the interval. Existence of global classical positive solutions is proved under general growth assumptions, with polynomial flocculation and deflocculation rates that guarantee uniform sup norm bounds for all time t obtained by an Lp−energy functional estimate. We also show finite time blow up can occur when the yield coefficients are large enough. Also, using arguments relying on the spectral and fixed theory, we show persistence and existence of nonhomogeneous population steady-states. Finally, we present some numerical simulations to show the combined effects of motility coefficients and the flocculation–deflocculation rates on the coexistence of species.

Copyright of Frontiers of Information Technology & Electronic Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we give criteria on the uniform boundedness of the solutions to linear difference equations (LEs) with periodic forcing functions. First, we give a necessary and sufficient condition that the sequence fLng of a square matrix L is bounded, from which a criterion on the uniform boundedness of the solutions to LEs is obtained. Second, a criterion on the uniform boundedness of the solutions for LEs with periodic forcing functions is given by applying a certain representation of solutions. In connection with LEs with delay, we give the characteristic equation of a matrix under the commuting condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the global behavior of classical solutions to the following two-species predator-prey chemotaxis model with signal-dependent diffusion and sensitivity$ \left\{\begin{array}{ll} u_{1t} = \nabla\cdot(d_{1}(v)\nabla u_{1})+ \nabla\cdot(\chi_{1}(v)u_{1}\nabla{v})+\mu_{1}u_{1}(1-u_{1}-e_{1}u_{2}), \\ u_{2t} = \nabla\cdot(d_{2}(v)\nabla u_{2})- \nabla\cdot(\chi_{2}(v)u_{2}\nabla{v})+\mu_{2}u_{2}(1+e_{2}u_{1}-u_{2}), \\ v_{t} = d_{3}\Delta{v}+\alpha u_{1}+\beta u_{2}-\gamma v \end{array}\right. $under homogeneous Neumann boundary condition in a bounded smooth domain \begin{document}$ \Omega\subset\mathbb{R}^{2} $\end{document}, where \begin{document}$ d_{3}, \; \mu_{1}, \; \mu_{2}, \; e_{1}, \; e_{2}, \; \beta, \; \gamma $\end{document} are positive constants, \begin{document}$ \alpha\in \mathbb{R} $\end{document}, and the functions \begin{document}$ d_{i}(v), \chi_{i}(v)(i = 1, 2) $\end{document} satisfy the following assumptions:(H1) \begin{document}$ d_{i}(v), \chi_{i}(v)\in C^{2}[0, \infty) $\end{document} satisfy \begin{document}$ d_{i}(v), \; \chi_{i}(v)>0 $\end{document} for \begin{document}$ v\geq0 $\end{document}, \begin{document}$ d'_{i}(v)<0 $\end{document} and \begin{document}$ \lim\limits_{v\rightarrow \infty}d_{i}(v) = 0 $\end{document}.(H2) The limits \begin{document}$ \lim\limits_{v\rightarrow \infty}\frac{\chi_{i}(v)}{d_{i}(v)} $\end{document} and \begin{document}$ \lim\limits_{v\rightarrow \infty}\frac{d'_{i}(v)}{d_{i}(v)} $\end{document} exist.We first apply the Moser iteration method to prove the uniform boundedness and global existence of solutions to the model. Then, by constructing appropriate Lyapunov functions, we establish the following ctiteria on the global asymptotic stability of the equilibria to the model: (i) If \begin{document}$ e_{1}<1 $\end{document} and both \begin{document}$ \mu_{1} $\end{document} and \begin{document}$ \mu_{2} $\end{document} are sufficiently large, the solution \begin{document}$ (u_1, u_2, v) $\end{document} converges to a unique positive equilibrium of the model. (ii) If \begin{document}$ e_{1}\geq 1 $\end{document} and \begin{document}$ \mu_{2} $\end{document} is large enough, the solution \begin{document}$ (u_1, u_2, v) $\end{document} converges to the semi-trivial equilibrium \begin{document}$ (0, 1, \frac{\beta}{\gamma}) $\end{document}. The respective convergence rates are at least exponential if \begin{document}$ e_1\neq1 $\end{document}, and algebraic if \begin{document}$ e_1 = 1 $\end{document}. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of cancer invasion model with nonlinear diffusion and remodeling of ECM. The primary difficulty that arises here is that due to nonlinear diffusion, the good coupling structure between the diffusion term and haptotactic term is destroyed, rendering the effective methods used in the linear diffusion model no longer applicable. Fortunately, we have found a new effective combination between the diffusion term and the haptotactic term, which allows the diffusion term to dominate the haptotactic term, thus preliminarily improving the regularity of the weak solution. Based on these results, we can prove part of long‐time asymptotic behavior of the solution, thereby finally proving the uniform boundedness of the weak solution. Subsequently, by improving the convergence of cancer cells u from Lp$L^p$‐norm to L∞$L^\infty$‐norm, it is also proved that after a long time, the weak solution will eventually be Hölder continuous for some slow diffusion cases. [ABSTRACT FROM AUTHOR]

In this article, we consider the parabolic system (ui)t=∇⋅(mUm−1A(∇ui,ui,x,t)+ℬ(ui,x,t)),(1≤i≤k){({u}^{i})}_{t}=\nabla \cdot (m{U}^{m-1}{\mathcal{A}}(\nabla {u}^{i},{u}^{i},x,t)+{\mathcal{ {\mathcal B} }}({u}^{i},x,t)),\hspace{1.0em}(1\le i\le k) in the range of exponents m>n−2nm\gt \frac{n-2}{n} where the diffusion coefficient UU depends on the components of the solution u=(u1,…,uk){\bf{u}}=({u}^{1},\ldots ,{u}^{k}). Under suitable structure conditions on the vector fields A{\mathcal{A}} and ℬ{\mathcal{ {\mathcal B} }}, we first showed the uniform L∞{L}^{\infty } boundedness of the function UU for t≥τ>0t\ge \tau \gt 0. We also proved the law of L1{L}^{1} mass conservation and the local continuity of solution u{\bf{u}}. In the last result, all components of the solution u{\bf{u}} have the same modulus of continuity if the ratio between UU and ui{u}^{i}, (1≤i≤k1\le i\le k), is uniformly bounded above and below.

This paper is concerned with the existence of a compact global attractor for a class of competition model in n−dimensional (n ≥ 1) domains. Using mathematical induction and more detailed interpolation estimates, especially Gagliardo-Nirenberg inequality, we obtain the existence of a compact global attractor, which implies the uniform boundedness of the global solutions. In particular, we get that the Shigesada-Kawasaki-Teramoto competition model has a compact global attractor for n < 10. The result of the S-K-T model extends the existence results of compact global attractor in [21] from n < 8 to n < 10, and extends the uniform boundedness results of the global solutions in [17] to the non-convex domain.

In this paper, we are dedicated to studying the global dynamics of a nonlocal predator–prey model with double mutation. First, by defining a pair of upper and lower solutions, we build a new comparison principle. Furthermore, based on the new comparison principle, we get the existence of the solutions by constructing monotone iterative sequences. Finally, using the quasi-fundamental solution, Gronwall's inequality and auxiliary functions, the uniqueness and uniform boundedness of the solutions are given. It is worth noting that this paper is the first to introduce the double mutation into the system and obtain the well-posedness and the uniform boundedness of the solutions by more detailed analysis and estimation. [ABSTRACT FROM AUTHOR]

Excellent student’s academic performance is the uppermost priority and goal of educators and facilitators. The dubious marginal rate between admission and graduation rates unveils the rates of dropout and withdrawal from school. To improve the academic performance of students, we optimize the performance indices to the dynamics describing the academic performance in the form of nonlinear system ODE. We established the uniform boundedness of the model and the existence and uniqueness result. The independence and interdependence equilibria were found to be locally and globally asymptotically stable. The optimal control analysis was carried out, and lastly, numerical simulation was run to visualize the impact of the performance index in optimizing academic performance. [ABSTRACT FROM AUTHOR]

This paper provides a uniform boundedness theorem for a class of convex operators, such as Banach–Steinhaus theorem for families of continuous linear operators. The case of continuous symmetric sublinear operators is outlined. Second, a general theorem characterizing the existence of the solution of the Markov moment problem is reviewed, and a related minimization problem is solved. Convexity is the common point of the two aims of the paper mentioned above. [ABSTRACT FROM AUTHOR]

This paper deals with classical solutions to the parabolicâ€"parabolic system u t = Î" (Îł (v) u) i n Ω Ă— (0 , ∞) , v t = Î" v âˆ' v + u i n Ω Ă— (0 , ∞) , ∂ u ∂ ν = ∂ v ∂ ν = 0 o n ∂ Ω Ă— (0 , ∞) , u (â‹... , 0) = u 0 , v (â‹... , 0) = v 0 i n Ω , where Ω is a smooth bounded domain in R n (n â©ľ 3), Îł (v) = v âˆ' k (k > 0) and the initial data (u 0, v 0) is positive and regular. This system has striking features similar to those of the logarithmic Kellerâ€"Segel system. It is established that classical solutions of the system exist globally in time and remain uniformly bounded in time if k ∈ (0, n /(n âˆ' 2)), independently of the magnitude of mass. This constant n /(n âˆ' 2) is conjectured as the optimal range guaranteeing global existence and boundedness in the corresponding logarithmic Kellerâ€"Segel system. In the course of our analysis we introduce an auxiliary function and derive an evolution equation that it satisfies. Using refined comparison estimates we control the behavior of the nonlinear term in the equation for the auxiliary function, and this in turn yields sufficient information to control solutions of the original system. [ABSTRACT FROM AUTHOR]

The proving of three big theorems, known as the uniform boundedness theorem, the open mapping theorem, and the closed graph theorem, is the pinnacle of any first functional analysis course. All three rely on the completeness of some or all of the spaces involved, and their proofs are based on Baire's theorem (or, the Baire category theorem), a topological conclusion. The aim of this paper is to prove the Uniform Boundedness Theorem without using Baire's Theorem and to show the logical dependence of these above three results on each other. [ABSTRACT FROM AUTHOR]

Baló's concentric sclerosis (BCS) is considered a variant of inflammatory demyelinating disease closely related to multiple sclerosis characterized by a discrete concentrically layered lesion in the cerebal white matter. Khonsari and Calvez (Plos ONE. 2(2007)) proposed a parabolic-elliptic-ODE chemotaxis model for BCS which describes the evolution of the densities of activated macrophages, cytokine and apoptotic oligodendrocytes. Because "classically activated" M1 microglia can produce cytotoxicity, we introduce a linear production term from the activated microglia in the ODE for pro-inflammatory cytotoxic. For the new BCS chemotaxis model, we first investigate the uniform boundedness and global existence of classical solutions, and then get a range of the chemosensitive rate χ where the unique positive equilibrium point is exponentially asymptotically stable.

Today industries related to finance are essentially implementing advanced mathematical tools. In 1973, Fisher Black and Myron Scholes developed an eminent stochastic model which later coined as Black-Scholes differential equations for option pricing. This paper illustrates a convenient time integration scheme based on the generalized trapezoidal formulas (GTF $[\alpha=\frac{1}{3}]$) introduced by Chawla et al. in 1996. GTF is applied for the temporal discretization along with the classical finite difference schemes in space direction. The proposed scheme yields the (uniform) stability employing the uniform bound of the inverse operator, as well as second-order spatial accuracy and third-order temporal accuracy under reasonable conditions. Finally, the numerical illustrations and comparison with existing schemes demonstrate the stability and accuracy of the method.

This paper provides a uniform boundedness theorem for a class of convex operators, such as Banach–Steinhaus theorem for families of continuous linear operators. The case of continuous symmetric sublinear operators is outlined. Second, a general theorem characterizing the existence of the solution of the Markov moment problem is reviewed, and a related minimization problem is solved. Convexity is the common point of the two aims of the paper mentioned above.

Suppose X is a variety defined over a finite extension K of Q p and suppose X admits a model X defined over the ring of integers R of K. Let f : X → X be an endomorphism of X defined over K that can be extended to an endomorphism of X defined over R. We apply a method of Fakhruddin to prove an explicit upper bound for the primitive period of periodic points defined over R. [ABSTRACT FROM AUTHOR]

The full information estimation (FIE) problem is addressed for discrete time-varying systems (TVSs) subject to the effects of a round-Robin (RR) protocol. A shared communication network is adopted for data transmissions between sensor nodes and the state estimator. In order to avoid data collisions in signal transmission, only one sensor node could have access to the network and communicate with the state estimator per time instant. The so-called RR protocol, which is also known as the token ring protocol, is employed to orchestrate the access sequence of sensor nodes, under which the chosen sensor node communicating with the state estimator could be modeled by a periodic function. A novel recursive FIE scheme is developed by defining a modified cost function and using a so-called “backward-propagation-constraints.” The modified cost function represents a special global estimation performance. The solution of the proposed FIE scheme is achieved by solving a minimization problem. Then, the recursive manner of such a solution is studied for the purpose of online applications. For the purpose of ensuring the estimation performance, sufficient conditions are obtained to derive the upper bound of the norm of the state estimation error (SEE). Finally, two illustrative examples are proposed to demonstrate the effectiveness of the developed estimation algorithm. [ABSTRACT FROM AUTHOR]

Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly super-) quadratic growth. This pushes forward the recent advances concerning global existence of reaction-diffusion systems dissipating mass in which a uniform-in-time bound has been known only in space dimension one or two. As an application, skew-symmetric Lotka-Volterra systems are shown to have unique classical solutions which are uniformly bounded in time in all dimensions with relatively compact trajectories in C(Ω)m. [ABSTRACT FROM AUTHOR]

In this work, we establish some new sufficient conditions to show the uniform h-stability for nonlinear time-varying perturbed systems which can be viewed as an extension of the uniform exponential stability and polynomial stability. Also, we study the boundedness of solutions when the origin is not necessarily an equilibrium point of the perturbed system. The idea is to use some Gronwall type integral inequalities. As an illustration, we present some examples with simulations to show the applicability of the obtained results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xinyang Normal University Natural Science Edition is the property of Journal of Xinyang Normal University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The safety of a vehicular platoon is seriously threatened in the presence of actuator saturations, (possibly fast) time‐varying non‐linear uncertainties. Meanwhile, the string stability and the strong string stability cannot eliminate the potential safety hazard caused by large initial error conditions. This study focuses on safety‐guaranteed distributed control of the vehicular platoon with a bidirectional communication topology and the constant time headway policy. The authors formulate bilateral inequality constraints on the spacing error between adjacent vehicles to represent the collision‐avoidance and compact formation performance. A novel state transformation technique is proposed to convert the bounded spacing error space to an unconstrained state space. On the basis, Comprehensive equality constraints for the transformed states are established by integrating the information of proximal (preceding and following) vehicles. In addition, an anti‐windup compensation method is utilised to handle actuator saturations. Then an adaptive constraint‐following controller is designed to render the uniform boundedness and uniform ultimate boundedness performance of the transformed state. As a result, the string stability, the strong string stability, the collision‐avoidance and compact formation are guaranteed despite the presence of actuator saturations and complex uncertainties. Numerical simulations are performed to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the quasilinear chemotaxis-haptotaxis model of cancer invasion { u t = ∇ ⋅ (D (u) ∇ u) + ∇ ⋅ (S 1 (u) ∇ v) + ∇ ⋅ (S 2 (u) ∇ w) + f (u , w) , x ∈ Ω , t > 0 , τ v t = Δ v − v + g 1 (w) g 2 (u) , x ∈ Ω , t > 0 , w t = − v w , x ∈ Ω , t > 0 in a bounded smooth domain Ω ⊂ R N (N ≥ 1) with zero-flux boundary conditions, where τ ∈ { 0 , 1 } , the functions D (u) , S 1 (u) , S 2 (u) ∈ C 2 ([ 0 , ∞)) , f (u , w) ∈ C 1 ([ 0 , ∞) 2) , g 1 (w) , g 2 (u) ∈ C 1 ([ 0 , ∞)) fulfill D (u) ≥ C D (u + 1) − α , S 1 (u) ≤ χ u (u + 1) β − 1 , S 2 (u) ≤ ξ u (u + 1) γ − 1 , f (u , w) ≤ u (a − μ u r − 1 − λ w) , f (0 , w) ≥ 0 , g 1 (w) ≥ 0 , 0 ≤ g 2 (u) ≤ K u κ with C D , χ , ξ , μ , K , κ > 0 , λ ≥ 0 , r > 1 and α , β , γ , a ∈ R. Under specific parameters conditions, it is shown that for any appropriately regular initial data, the associated initial-boundary value problem admits a globally bounded classical solution. Moreover, when f = u (a − μ u r − 1 − λ w) , g 1 (w) ≡ 1 and g 2 (u) = u κ , the asymptotic stability of solutions is also investigated. Specifically, for some a 0 , μ 0 > 0 independent of (u 0 , v 0) , the bounded classical solution (u , v , w) exponentially converges to ((a μ) 1 r − 1 , (a μ) κ r − 1 , 0) in L p (Ω) × L ∞ (Ω) × W 1 , ∞ (Ω) for any p ≥ 2 if a > a 0 and μ > μ 0. These results improve or extend previously known ones, and partial results are new. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study global solutions to the following strongly coupled systems: {ut=∇⋅(D1∇u−χu∇v)+(a1−b1u−c1v)u,x∈Ω,t>0,0=D2Δv+(a2−b2u−c2v)v,x∈Ω,t>0, $$\textstyle\begin{cases} u_{t}=\nabla\cdot(D_{1} \nabla u -\chi u \nabla v)+(a_{1}-b_{1}u-c_{1}v)u,\quad x \in\Omega,t>0, \\ 0=D_{2}\Delta v+(a_{2}-b_{2}u-c_{2}v)v,\quad x \in\Omega,t>0, \end{cases} $$ over Ω⊂RN $\Omega\subset\mathbb{R}^{N}$, N≥2 $N\geq2$, subject to homogeneous Neumann boundary conditions and nonnegative initial data. Here Di $D_{i}$, ai $a_{i}$, bi $b_{i}$ and ci $c_{i}$, i=1,2 $i=1,2$, are positive constant. It is proved that this system admits global and bounded classical solutions for all χ>0 $\chi>0$. We also prove the global well-posedness for its repulsive counterpart {ut=∇⋅(D1∇u+χu∇v)+(a1−b1u−c1v)u,x∈Ω,t>0,0=D2Δv+(a2−b2u−c2v)v,x∈Ω,t>0, $$\textstyle\begin{cases} u_{t}=\nabla\cdot(D_{1} \nabla u +\chi u \nabla v)+(a_{1}-b_{1}u-c_{1}v)u,\quad x \in\Omega,t>0, \\ 0=D_{2}\Delta v+(a_{2}-b_{2}u-c_{2}v)v,\quad x \in\Omega,t>0, \end{cases} $$ provided that b1>a2b2χ(N−2)c2D2N $b_{1}>\frac{a_{2}b_{2} \chi(N-2)}{c_{2}D_{2} N}$. Our results extend (Discrete Contin. Dyn. Syst. 35:1239–1284, 2015) to higher dimensions and to its repulsive case.

In this paper, we consider the following system { u t = Δ u − χ ∇ ⋅ (u ∇ ω) , v t = d v Δ v − ξ ∇ ⋅ (v ∇ ω) , m t = d m Δ m + u − m , ω t = − (γ 1 u + m) ω , in two dimensional space with zero-flux boundary conditions. This model was proposed by Franssen et al. [7] to characterize the invasion and metastatic spread of cancer cells. We first establish the global existence of uniformly bounded global strong solutions. Then using the decay of ECM and the positivity of MDE, we further improve the regularity of obtained solutions, and achieve the uniform boundedness of solutions in the classical sense. Subsequently, we also prove the uniqueness of solutions. After that, we turn our attention to the large time behavior of solutions, and show that the global classical solution strongly converges to a semi-trivial steady state in the large time limit. [ABSTRACT FROM AUTHOR]

This work is concerned with the Neumann initial boundary value problem and Cauchy problem of a parabolic p‐Laplacian equation with nonlocal Fisher–KPP type reaction terms. We establish a uniform boundedness and global existence of solutions to the equation by applying the method of multipliers and modified Moser's iteration technique for some ranges of parameters. The ranges of parameters have similar structure to that of the classical critical Fujita exponent. [ABSTRACT FROM AUTHOR]

We generalize the results of Abtahi and Farhangi about the joint spectrum and A-valued spectrum of a vector-valued map from the class of unital commutative semisimple Banach algebras to the case of unital topological algebras. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we develop an adaptive control algorithm for addressing security for a class of networked vehicles that comprise a formation of n^ human‐driven vehicles sharing kinematic data and an autonomous vehicle in the aft of the vehicle formation receiving data from the preceding vehicles through wireless vehicle‐to‐vehicle communication devices. Specifically, we develop an adaptive controller for mitigating time‐invariant state‐dependent adversarial sensor and actuator attacks while guaranteeing uniform ultimate boundedness of the closed‐loop networked system. Furthermore, an adaptive learning framework is presented for identifying the state space model parameters based on input‐output data. This learning technique utilizes previously stored data as well as current data to identify the system parameters using a relaxed persistence of excitation condition. The effectiveness of the proposed approach is demonstrated by an illustrative numerical example involving a platoon of connected vehicles. [ABSTRACT FROM AUTHOR]

A novel robust approach for the obedience control of Furuta pendulum with uncertainty is proposed. The uncertainty considered in this paper is (possibly fast) time-varying and bounded, which may exist in any stage of the pendulum subsystem. By the Lagrangian formulation of the nonlinear pendulum system, a robust control, based on a general Lyapunov function, is designed to render the Furuta pendulum a position obedience. As a consequence of the Lyapunov approach, the control design is not restricted to linearize the pendulum system. The system performance under the proposed control is guaranteed as uniform boundedness and uniform ultimate boundedness. The salient features of this new control are demonstrated both analytically and numerically. The experiment is conducted in the Furuta pendulum system to prove the validity and effectiveness of the control design. [ABSTRACT FROM AUTHOR]