Sufficient Conditions For Robust Stability Research Articles

Robust Stability of Uncertain Takagi-Sugeno Fuzzy Systems with Time-varying Input-delay

This paper aims to design a controller to robustly stabilize uncertain Takagi-Sugeno fuzzy systems with time-varying input delay. Based on Lyapunov-Krasovskii functional approach, the sufficient conditions for robust stabilization of such systems are given in the form of linear matrix inequalities. The controller design does not have to require that the time-derivative of time-varying input delay be smaller than one. A numeric example is given to show that the proposed results are effective and less conservative.

Robust Stability and Synthesis of Nonlinear Discrete Control Systems under Uncertainty

With the use of Lyapunov functions chosen as the norm of state vector, we obtain the robust stability sufficient conditions for a wide class of nonlinear, and generally nonstationary, discrete-time control systems with the given set-valued parameter estimates. For a strictly monotone nonlinear function, validation of these conditions is equivalent to solution of a series of combinatorial problem in the state space.Synthesis of robustly stable control systems in a domain is performed on the basis of the obtained sufficient conditions of robust stability.

An LMI approach for robust stability of genetic networks

This paper addresses the problem of establishing robust stability of uncertain genetic networks with SUM regulatory functions. For these networks we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity, and we show that this condition can be formulated as a linear matrix inequality (LMI) optimization obtained via the square matricial representation (SMR) of polynomials by adopting polynomial Lyapunov functions and polynomial descriptions of the bounding set. Then, we propose a method for computing a family of bounding sets by means of convex optimizations. It is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed being the solution of a system of parameter-dependent nonlinear equations, and is hence unknown.

Robust Semiglobal Stabilization of the Second Order System by Relay Feedback with an Uncertain Variable Time Delay

We present sufficient conditions for robust relay-delayed semiglobal stabilization of second order systems, which relate the upper bound to an uncertain time delay and the parameters of the plant. We also suggest an algorithm of delayed relay control gain adaptation for semiglobal stabilization, which is based on delayed information about the sign of the controlled variable only. The proposed algorithm suppresses bounded uncertainties in the time delay; that is, being designed for the upper bound of uncertainty in the time delay, the control law ensures semiglobal stabilization independently of any variable time delay obeying the given upper bound.

Robust stability analysis of adaptive control based on recurrent ANN

Adaptive control by means of neural networks for non-linear dynamical systems is an open issue. For real world applications, practitioners have to pay attention to external disturbances, parameters uncertainty and measurement noise, as long as these factors will influence the stability of the closed loop system. As a consequence, robust stability of the closed loop controlled by neural network is an important issue that must be considered. Our contribution concerns the robustness analysis and synthesis of adaptive indirect control scheme. This scheme is based on fully connected neural networks, and inspired from the standard real time recurrent learning. This analysis is concerned by combining Lyapunov approach and linearisation around the nominal parameters to establish analytical sufficient conditions for the global robust stability of adaptive neural network controller. Advantages of the proposed algorithm are suggested according to simulation examples.

Conservatism-free Robust Stability Check of Fractional-order Interval Linear Systems

This paper addresses a necessary and sufficient robust stability condition of fractional-order interval linear time invariant systems. The state matrix A is considered as a parametric interval uncertain matrix and fractional commensurate order is considered belonging to 1 ≤ α < 2. Using the existence condition of Hermitian matrix P = P* for a complex Lyapunov inequality, we show that a fractional-order interval linear system is robust stable if and only if there exist Hermitian matrices P = P* such that complex Lyapunov inequalities are satisfied for all vertex matrices, which is a set of selected matrices. Two numerical examples are presented to verify the validity of the proposed approach.

Robust stability analysis of static neural network with S-type distributed delays

In this paper, we investigate local robust stability of static neural network (SNN) with S-type distributed delays. We derive some new sufficient conditions for local robust stability of equilibrium points and estimate attracting domains of equilibrium points except isolated equilibrium points. Our results not only show local robust stability of equilibrium points but also allow much broader application for static neural network with or without delays. It is shown that our results are new and improve corresponding results existing in the previous literature.

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.

Robust H∞ control of uncertain linear impulsive stochastic systems

AbstractThis paper develops robust stability theorems and robust H∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Delay-dependent robust stability of linear systems with non-commensurate time varying delays

In this article we investigate the robust stability of uncertain systems with non-commensurate time varying delays. Two types of perturbations are considered. First, we consider time varying and unknown but norm bounded uncertainties. Next systems with polytopic-type uncertainties are studied. Based on Finsler's lemma we propose a new method for achieving less restrictive sufficient conditions for delay-dependent robust stability. The results are presented in terms of linear matrix inequalities. Three examples are given for illustration and comparison with previous results.

On input-to-state stability of min–max nonlinear model predictive control

In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and other disturbance inputs. The min–max model predictive control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for robust stability of the resulting closed-loop system using the input-to-state stability (ISS) framework. First, we show that only input-to-state practical stability can be ensured in general for closed-loop min–max MPC systems; and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new conditions for guaranteeing ISS of min–max MPC closed-loop systems, using a dual-mode approach. An example illustrates the presented theory.

Robust H∞ Networked Control for Uncertain Fuzzy Systems with Time-delay

A robust H ∞ networked control method for Takagi-Sugeno (T-S) fuzzy systems with uncertainty and time delay is presented. A state feedback controller is designed via the networked control system (NCS) theory. Sufficient condition for robust stability with H ∞ performance is obtained. Network-induced delay in network transmission and packet dropout are analyzed. Simulation result shows the validity of this control scheme.

T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems

This paper proposes a fuzzy bilinear model for a class of nonlinear systems and a fuzzy controller to stabilize such systems. By examination of a modeling problem, we describe how to transform a nonlinear system into a bilinear one via Taylor's series expansion and then we adopt the Takagi-Sugeno (T-S) fuzzy modeling technique to construct a fuzzy bilinear model. For controller design, the parallel distributed compensation (PDC) method is utilized to stabilize the fuzzy bilinear system (FBS), and some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Moreover, we propound some sufficient conditions for robust stabilization of the FBS with parametric uncertainties. Finally, a numerical example and the Van de Vusse model are utilized to demonstrate the validity and effectiveness of the proposed FBS.

New Sufficient Conditions for Global Robust Stability of Delayed Neural Networks

In this paper, we continue to explore application of nonsmooth analysis to the study of global asymptotic robust stability (GARS) of delayed neural networks. In combination with Lyapunov theory, our approach gives several new types of sufficient conditions ensuring GARS. A significant common aspect of our results is their low computational complexity. It is demonstrated that the reported results can be verified either by conducting spectral decompositions of symmetric matrices associated with the uncertainty sets of network parameters, or by solving a semidefinite programming problem. Nontrivial examples are constructed to compare with some closely related existing results

Robust PID Decentralized Controller Design Using LMI

The new LMI based method for robust stability analysis for linear uncertain system with PID controller is proposed. The general constrained structure of controller matrix is considered appropriate for both output feedback and decentralized control and the respective guaranteed cost control design scheme is presented. The sufficient robust stability condition is developed for extended quadratic performance index including first derivative of the state vector to damp oscillations. The obtained stability condition is formulated for parameter-dependent Lyapunov function.

Robust stability and performance for interval process plants

In this paper, a two-degrees-of-freedom control design methodology for interval plants to guarantee both the robust stability and performance has been considered. A simple necessary condition and sufficient condition for robust Hurwitz stability of interval polynomial has been obtained using the results of Nie [Nie YY. A new class of criterion for the stability of the polynomials. Acta Mechnica Sinica 1976;110–6] for fixed polynomials. The proposed design methodology based on the obtained necessary condition and sufficient condition is then applied to design a robust control system for a second-order unstable plant in the presence of unknown but bounded parameter uncertainties. Subsequently, a pre-filter is constructed to ensure the desired system performance. Simulation results are used to establish the efficacy of the proposed method for interval plants.

Necessary and sufficient conditions for robust oscillatory stability

The problem of robust oscillatory stability of uncertain systems is investigated in this article. For the uncertain systems, whose characteristic polynomial sets belong to the interval polynomial family or diamond polynomial family, sufficient and necessary conditions are given based on the stability and/or oscillation properties of some special extreme point polynomials. A systematic approach exploiting Yang's complete discrmination system is proposed to check the robust oscillatory stability of such uncertain systems. The proposed method is efficient in computation and can be easily implemented.

Delay-dependent robust stabilization for uncertain neutral systems with distributed delays

The problems of robust stability and robust stabilization of uncertain neutral systems with distributed delays are studied in this paper. Using a combination of integral inequality technique and descriptor system approach, new delay-dependent sufficient conditions for robust stability and robust stabilization are formulated in terms of linear matrix inequalities (LMIs). LMI-based conditions are also derived for robust stability and robust stabilizability of uncertain distributed-delay systems when the distributed delay belongs to a given interval. When the results obtained in this paper are applied to stabilization of combustion in the chamber of a liquid monopropellant rocket motor, it is found that the combustion can be robustly stabilized over larger variation intervals of pressure parameter and time-delay parameter than those obtained in Zheng and Frank [(2002). Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica, 38, 487–497].

Robust stability of FET circuits at high frequency

A necessary and sufficient condition for robust stability of a group of electronic circuits at high frequency that contain of source-coupled pairs is proposed. When a source-coupled pair is used as a single input–output unit, it has uncertainty in its transfer function at high frequencies. This uncertainty can cause instability in closed-loop electronic circuits and is modelled as multiplicative perturbation in the transfer function of the source-coupled pair. Based on this uncertainty model, a necessary and sufficient condition for robust stability in these electronic circuits is presented. This condition guarantees internal stability of these electronic circuits at this frequency.

Robust control of gas tungsten arc welding system

The robust control law for gas tungsten arc welding dynamic process,which is a typical sampled-data system and full of uncertainties,is presented.By using the Lyapunov second method, the robust control and robust optimal control for a class of sampled-data systems whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain.As a result,some sufficient conditions of robust stability and the corresponding robust control laws are derived.All these results are designed by solving a class of linear matrix inequalities(LMIs)and a class of dynamic optimization problem with LMIs constraints respectively.An example adapted under some experimental conditions in the dynamic process of gas tungsten arc welding system in which the controlled variable is the backside width of weld pool and controlling variable pulse duty ratio,is worked out to illustrate the proposed results,it is shown that the sampling period is the crucial design parameter.