Search results for "Lyapunov function"
showing 10 items of 104 documents
Sliding Intermittent Control for BAM Neural Networks with Delays
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/615947 Open Access This paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuou…
Neural Petri Control: an application on a mobile robot
2006
In the present work, an innovative nonlinear controller of nonholonomic mechanical systems, characterized by a dynamic not well known model a priori, using a new neural model obtained by the combination of a Petri net with a neural network, is proposed. The performances of the control algorithm are evaluated for tasks of tracking of time trajectories. The study of the stability of the total system to closed loop is based on the Lyapunov theory. Simulation experiments, made taking into consideration a nonholonomic mobile robot, to two wheels, allowed to verify the theoretical results.
On the variations of the Betti numbers of regular levels of Morse flows
2011
Abstract We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Betti numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z p Z with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds.
Robust reliable passive control of uncertain stochastic switched time-delay systems
2014
This paper investigates the problem of robust reliable passive control for a class of uncertain stochastic switched time-delay systems with actuator failures. The multiple Lyapunov functions (MLFs) technique is exploited to derive a delay-dependent sufficient condition for the stochastic switched time-delay systems to be passive and exponentially stable under a state-based switching law. Moreover, the proposed approach is extended to investigate stochastic switched systems with structured uncertainties. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.
The Lyapunov dimension formula for the global attractor of the Lorenz system
2015
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …
Robust L1 fixed-order filtering for switched LPV systems with parameter-dependent delays
2015
Abstract This paper is concerned with the L1 fixed-order filtering problem for a class of switched linear parameter-varying (LPV) systems in which the system matrices and the time delays are dependent on the real-time measured parameters. The authors׳ attention is concentrated on designing the fixed-order filter that guarantees the filtering error system to be exponentially stable and to satisfy a prescribed L1 disturbance attenuation level with respect to all amplitude-bounded disturbances. Based on the switching logic with the minimum average dwell time (ADT), the delay-dependent L1 performance criterion for the switched LPV systems is first established. As there exists coupling between a…
On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems
2014
This paper deals with the problem of robust stability and robust stabilization for a class of continuous-time singular Takagi-Sugeno fuzzy systems. Sufficient conditions on stability and stabilization are proposed in terms of strict LMI (Linear Matrix Inequality) for uncertain T-S fuzzy models. In order to reduce the conservatism of results developed using quadratic method, an approach based on non-quadratic Lyapunov functions and S-procedure is proposed. Illustrative examples are given to show the effectiveness of the given results Refereed/Peer-reviewed
Fuzzy/Kalman Hierarchical Horizontal Motion Control of Underactuated ROVs.
2010
A new closed loop fuzzy motion control system including on-line Kalman's filter (KF) for the two dimensional motion of underactuated and underwater Remotely Operated Vehicle (ROV) is presented. Since the sway force is unactuated, new continuous and discrete time models are developed using a polar transformation. A new hierarchical control architecture is developed, where the high level fuzzy guidance controller generates the surge speed and the yaw rate needed to achieve the objective of planar motion, while the low level controller gives the thruster surge force and the yaw torque control signals. The Fuzzy controller ensures robustness with respect to uncertainties due to the marine envi…
Semiglobal practical integral input-to-state stability for a family of parameterized discrete-time interconnected systems with application to sampled…
2015
Abstract Semiglobal practical integral input-to-state stability (SP-iISS) for a feedback interconnection of two discrete-time subsystems is given. We construct a Lyapunov function from the sum of nonlinearly-weighted Lyapunov functions of individual subsystems. In particular, we consider two main cases. The former gives SP-iISS for the interconnected system when both subsystems are semiglobally practically integral input-to-state stable. The latter investigates SP-iISS for the overall system when one of subsystems is allowed to be semiglobally practically input-to-state stable. Moreover, SP-iISS for discrete-time cascades and a feedback interconnection including a semiglobally practically i…
A differential equation approach to implicit sweeping processes
2019
International audience; In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.