Fernando de Oliveira Souza

Technical communique: Reducing conservativeness in recent stability conditions of TS fuzzy systems

In this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous-time Takagi-Sugeno fuzzy systems based on fuzzy Lyapunov functions is proposed. This new strategy generalizes previous results.

New Stability Conditions Based on Piecewise Fuzzy Lyapunov Functions and Tensor Product Transformations

Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed. The key idea is to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions. By relying on these special local transformations, the associated linear matrix inequalities that are used to prove the systems stability can be relaxed without increasing the number of conditions. In addition, to enhance the usefulness of the proposed methodology, one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives. A standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases.

On Stability and Stabilization of T–S Fuzzy Time-Delayed Systems

In this paper, the stability analysis and control design of Takagi-Sugeno (TS) fuzzy systems subject to uncertain time-delay are addressed. The proposed approach is based on linear matrix inequalities and the Lyapunov-Krasovskii theory, where a new fuzzy weighting-dependent Lyapunov-Krasovskii functional is introduced. By employing the Gu discretization technique and strategies to add slack matrix variables, less conservative conditions are obtained. Numerical experiments are performed to illustrate the effectiveness of the proposed methodology.

Brief paper: Stability independent of delay using rational functions

This paper is concerned with the problem of assessing the stability of linear systems with a single time-delay. Stability analysis of linear systems with time-delays is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we show that a linear system with a single time-delay is stable independent of delay if and only if a certain rational function parameterized by an integer k and a positive real number T has only stable roots for any finite T>=0 and any k>=2. We then show how this stability result can be further simplified by analyzing the roots of an associated polynomial parameterized by a real number @d in the open interval (0,1). The paper is closed by showing counterexamples where stability of the roots of the rational function when k=1 is not sufficient for stability of the associated linear system with time-delay. We also introduce a variation of an existing frequency-sweeping necessary and sufficient condition for stability independent of delay which resembles the form of a generalized Nyquist criterion. The results are illustrated by numerical examples.

Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov-Krasovskii theory

This paper presents a new approach to the analysis of asymptotic stability of artificial neural networks (ANN) with multiple time-varying delays subject to polytope-bounded uncertainties. This approach is based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz-Newton model based transformation without including any additional dynamics. Three examples with numerical simulations are used to illustrate the effectiveness of the proposed method. The first example considers the neural network with multiple time-varying delays, which may be seen as a particular case of the second example where it is subject to uncertainties and multiple time-varying delays. Finally, the third example analyzes the stability of the neural network with higher numbers of neurons subject to a single time-delay. The Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability in the bifurcation point.

On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

Abstract This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.

Improved robust ℋ ∞ control for neutral systems via discretised Lyapunov-Krasovskii functional

This paper deals with the robust stability analysis and robust control synthesis with guaranteed performance index for time-invariant uncertain neutral systems based on linear matrix inequalities (LMIs). The novelty is to extend the discretisation technique introduced by K. Gu for an appropriate parameter-dependent Lyapunov–Krasovskii functional. Then, the approach proposed improves the previous criteria from the literature that treats robust stability and control for uncertain neutral systems. The main strategy used to derive the obtained conditions is to introduce slack variables allowing one to decouple the system matrices from the Lyapunov functional matrices, without including additional dynamics. Two numerical examples are performed to support the theoretical predictions. The first example deals with stability analysis and the other illustrates how the proposed approach may provide a better solution for the ℋ ∞ guaranteed cost control problem when compared with others available in the literature.

Conditions for Consensus of Multi-Agent Systems With Time-Delays and Uncertain Switching Topology

This paper proposes a new approach for the analysis of consensus of multi-agent systems subject to time-varying delayed control inputs and switching topology. The main contribution is a condition for consensus for a networked system based on linear matrix inequalities that takes into account the joint effect of time-varying delays and switching network topology. Topology changes are modeled using Markov jumps with uncertain rates of transitions. A practical example is shown to illustrate the main result in various scenarios.

Synchronisation of chaotic delayed artificial neural networks: an ℍ ∞ control approach

This article presents a new linear matrix inequality-based approach to an ℋ∞ output feedback control problem of master—slave synchronisation of artificial neural networks with uncertain time-delay, which can exhibit chaotic behaviour. The uncertain time-delay is considered as a composition of a nominal positive value subject to a time-varying perturbation. The methodology to be employed is based on the selection of a new discretised Lyapunov–Krasovskii functional (LKF) with two parts: the first is related to the nominal delay, and the second one is related to the time-varying perturbation. Extra manipulations allows us to introduce free matrices decoupling the LKF matrices from the system matrices, turning to obtain a control design condition easier. Finally, an insightful numeric simulation will be proposed to show the effectiveness of this kind of methodology to the problem of synchronising coupled chaotic delayed artificial neural networks. Besides, based on the information transmission via control principle, two information transmission experiments are performed as a possible application or/and an index to measure the effectiveness of the proposed approach.

New delay-interval stability condition

The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, τ]. The case of unstable delayed systems for r = 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.