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On the optimal continuous decentralized control of non-linear dynamical multivariable systems about the origin.

Manuel de la Sen Parte (1987)

Trabajos de Investigación Operativa

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...

On the relation of delay equations to first-order hyperbolic partial differential equations

Iasson Karafyllis, Miroslav Krstic (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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...

On the solution of the constrained multiobjective control problem with the receding horizon approach

Daniele De Vito, Riccardo Scattolini (2008)

Kybernetika

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...

On the stability of neutral-type uncertain systems with multiple time delays

Pin-Lin Liu (2005)

International Journal of Applied Mathematics and Computer Science

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...

On the stability of T-S fuzzy control for non-linear systems.

Zoe Doulgeri, John B. Theocharis (2000)

Mathware and Soft Computing

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...

On the stabilization of laminated beams with delay

Kassimu Mpungu, Tijani A. Apalara, Mukhiddin Muminov (2021)

Applications of Mathematics

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.

On the stabilization problem for nonholonomic distributions

Ludovic Rifford, Emmanuel Trélat (2009)

Journal of the European Mathematical Society

Let M be a smooth connected complete manifold of dimension n , and Δ be a smooth nonholonomic distribution of rank m ≤ 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 Δ 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...

On the state observation and stability for uncertain nonlinear systems

Mohamed Ali Hammami (2000)

Kybernetika

In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [3,2,1,4]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.

On the static output feedback stabilization of deterministic finite automata based upon the approach of semi-tensor product of matrices

Zhipeng Zhang, Zengqiang Chen, Xiaoguang Han, Zhongxin Liu (2018)

Kybernetika

In this paper, the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) via the semi-tensor product (STP) of matrices is investigated. Firstly, the matrix expression of Moore-type automata is presented by using STP. Here the concept of the set of output feedback feasible events (OFFE) is introduced and expressed in the vector form, and the stabilization of DFA is defined in the sense of static output feedback (SOF) control. Secondly, SOFS problem of DFA is investigated...

On timed event graph stabilization by output feedback in dioid

B. Cottenceau, Mehdi Lhommeau, Laurent Hardouin, Jean-Louis Boimond (2003)

Kybernetika

This paper deals with output feedback synthesis for Timed Event Graphs (TEG) in dioid algebra. The feedback synthesis is done in order to (1) stabilize a TEG without decreasing its original production rate, (2) optimize the initial marking of the feedback, (3) delay as much as possible the tokens input.

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