We consider a finite-dimensional control system $\left(\Sigma \right)\dot{x}\left(t\right)=f(x\left(t\right),u\left(t\right))$, such that there exists a feedback stabilizer $k$ that renders $\dot{x}=f(x,k\left(x\right))$ globally asymptotically stable. Moreover, for $(H,p,q)$ with $H$ an output map and $1\le p\le q\le \infty$, we assume that there exists a ${𝒦}_{\infty }$-function $\alpha$ such that $\parallel H\left(x_u\right){\parallel }_q\le {\alpha (\parallel u\parallel }_p)$, where $x_u$ is the maximal solution of ${\left(\Sigma \right)}_k\dot{x}\left(t\right)=f(x\left(t\right),k\left(x\left(t\right)\right)+u\left(t\right))$, corresponding to $u$ and to the initial condition $x\left(0\right)=0$. Then, the gain function $G_{(H,p,q)}$ of $(H,p,q)$ given by$$G_{(H,p,q)}\left(X\right)\stackrel{\mathrm{def}}{=}\underset{{\parallel u\parallel }_p=X}{sup}{\parallel H\left(x_u\right)\parallel }_q,$$is well-defined. We call profile of $k$ for $(H,p,q)$ any ${𝒦}_{\infty }$-function which is of the same order of magnitude as $G_{(H,p,q)}$. For the double integrator...

We consider a finite-dimensional control system $\left(\Sigma \right)\dot{x}\left(t\right)=f(x\left(t\right),u\left(t\right))$, such that there exists a feedback stabilizer k that renders $\dot{x}=f(x,k\left(x\right))$ globally asymptotically stable. Moreover, for (H,p,q) with H an output map and $1\le p\le q\le \infty$, we assume that there exists a ${𝒦}_{\infty }$-function α such that $\parallel H\left(x_u\right){\parallel }_q\le {\alpha (\parallel u\parallel }_p)$, where xu is the maximal solution of ${\left(\Sigma \right)}_k\dot{x}\left(t\right)=f(x\left(t\right),k\left(x\left(t\right)\right)+u\left(t\right))$, corresponding to u and to the initial condition x(0)=0. Then, the gain function $G_{(H,p,q)}$ of (H,p,q) given by 14.5cm $$G_{(H,p,q)}\left(X\right)\stackrel{\mathrm{def}}{=}\underset{{\parallel u\parallel }_p=X}{sup}{\parallel H\left(x_u\right)\parallel }_q,$$ is well-defined. We call profile of k for (H,p,q) any ${𝒦}_{\infty }$-function which is of the same order of...

We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

This paper deals with the local (around the equilibrium) optimal decentralized control of autonomous multivariable systems of nonlinearities and couplings between subsystems which can be expressed as power series in the state-space are allowed in the formulation. They only affect for the optimal performance integrals in cubic and higher terms in the norm of the initial conditions of the dynamical differential system. The basic hypothesis which is made is that the system is centrally-stabilizable...

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on...

This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem...

The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness...

This work concerns the stability analysis of a non-linear system controlled by a fuzzy T-S control law. It is shown that the closed loop system is in general expressed by a T-S fuzzy system composed of rules with affine linear systems in their consequent parts. The stability of affine T-S systems is then investigated for a special case using as an example the regulation problem of single link robot arm. Stability conditions are derived using the indirect and direct Lyapunov method and simulation...

We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.

We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.

In this paper, we consider some classes of bilinear systems. We give sufficient condition for the asymptotic stabilization by using a positive and a negative feedbacks.

Of concern in this paper is the laminated beam system with frictional damping and an internal constant delay term in the transverse displacement. Under suitable assumptions on the weight of the delay, we establish that the system's energy decays exponentially in the case of equal wave speeds of propagation, and polynomially in the case of non-equal wave speeds.

Let $M$ be a smooth connected complete manifold of dimension $n$, and $\Delta$ be a smooth nonholonomic distribution of rank $m\le n$ on $M$. We prove that if there exists a smooth Riemannian metric on1for which no nontrivial singular path is minimizing, then there exists a smooth repulsive stabilizing section of $\Delta$ on $M$. Moreover, in dimension three, the assumption of the absence of singular minimizing horizontal paths can be dropped in the Martinet case. The proofs are based on the study, using specific results of...