### A new robust training law for dynamic neural networks with external disturbance: an LMI approach.

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In this paper, we study decentralized ${H}_{\infty}$ feedback control systems with quantized signals in local input-output (control) channels. We first assume that a decentralized output feedback controller has been designed for a multi-channel continuous-time system so that the closed-loop system is Hurwitz stable and a desired ${H}_{\infty}$ disturbance attenuation level is achieved. However, since the local measurement outputs are quantized by a general quantizer before they are passed to the controller, the system’s...

In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The dynamics of the active leader is given in a general form of linear system. The switching interconnection topology with communication delay among the agents is taken into consideration. A neighbor-based estimator is designed for each agent to obtain the unmeasurable state variables of the dynamic leader, and then a distributed feedback control law is developed to achieve consensus....

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system...

The concepts of stability, attractivity and asymptotic stability for systems subject to restrictions of the input values are introduced and analyzed in terms of Lyapunov functions. A comparison with the well known input-to-state stability property introduced by Sontag is provided. We use these concepts in order to derive sufficient conditions for global stabilization for triangular and feedforward systems by means of saturated bounded feedback controllers and also recover some recent results...

We consider the system $\u1e8b\left(t\right)-\int {\u2080}^{\eta}dR\u0303\left(\tau \right)\u1e8b(t-\tau )={\int}_{0}^{\eta}dR\left(\tau \right)x(t-\tau )+\left[Fx\right]\left(t\right)+u\left(t\right)$ (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...

We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine.

This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...

The problem of invariant output tracking is considered: given a control system admitting a symmetry group $G$, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of $G$. Invariant output errors are defined as a set of scalar invariants of $G$; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required...

The problem of invariant output tracking is considered: given a control system admitting a symmetry group G, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of G. Invariant output errors are defined as a set of scalar invariants of G; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the...

Multi-level saturation feedbacks induce nonlinear disturbance-to-state L2 stability for nonlinear systems in feedforward form. This class of systems includes linear systems with actuator constraints.

This paper considers the problem of output control of nonlinear delay systems by means of state delayed feedback. In previous papers, through the use of a suitable formalism, standard output control problems, such as output regulation, trajectory tracking, disturbance decoupling and model matching, have been solved for a class of nonlinear delay systems. However, in general an output control scheme does not guarantee internal stability of the system. Some results on this issue are presented in this...

New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference...