Sufficient Conditions For Robust Stability Research Articles

Data-driven Adaptive Control: Making Unfalsified Control Work Better

AbstractIn this paper, a data-driven adaptive control scheme is presented which is based upon Unfalsified Control theory. The presented work extends our previous works on suitable cost functions in Unfalsified Control and the use of optimization to obtain new optimal controllers. A data-driven method is used here to obtain a sufficient condition for robust stability. This condition is used to falsify the non-robust controllers. Additionally it is used along with a signal-to-peak norm constraint in the optimization of the candidate controller parameters, to obtain robust controllers and to avoid the controller saturation. A case study using a well known example from chemical engineering shows the application of the extended scheme.

Robust Reliable H∞ Control for a Class of Nonlinear Perturbed Systems with Electrical Application: An LMI Approach

AbstractThis paper discusses the robust feedback control for a class of nonlinear polynomial systems with H∞ robustness performance. The studied systems are described by perturbed polynomial models based on the Kronecker product and the Kronecker power of the state vector. The proposed nonlinear feedback control scheme is developed to provide the practical stability of the closed loop system using the well-known second Lyapunov method with quadratic function. A sufficient condition for robust stabilization and H∞ control performance is given such that ultimately bounds on the controlled system trajectories are ensured and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. The developed control approach is formulated as a minimization problem and derived in the form of Linear Matrix Inequalities (LMIs). To asses the performances of the proposed control method through numerical simulations, a power electrical application is chosen to provide the effectiveness of the proposed methodology.

Robust Stability Analysis for Uncertain Switched Discrete‐Time Systems

This paper is concerned with the robust stability for a class of switched discrete‐time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete‐time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete‐time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

New Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time‐Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time‐varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

Sufficient Conditions for Robust Input-Output Finite-Time Stability of Linear Systems in Presence of Uncertainties

AbstractThe concept of Bounded-Input Bounded-Output (BIBO) stability arises when one wants to focus on the study of the the input-output behavior of a dynamical system, as opposed to the classical Lyapunov stability. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS. A system is said to be IO finite time stable if, assigned a bounded input class and some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. IO-FTS has been already investigated in previous papers, whereas this is the first work dealing with the input-output behavior of an uncertain dynamical system in the FTS framework. Two sufficient conditions are given, concerning the class of 2 and ∞ input signals, for the analysis of robust IO-FTS. The applicability of the results is illustrated by means of a numerical examples.

Decoupling Smith Control for Multivariable System with Time Delays

AbstractIn order to solve the decoupling control problem of multivariable system with time delays, a new decoupling Smith control method for multivariable system with time delays was proposed. Firstly, the decoupler based on the adjoint matrix of the multivariable system model with time delays was introduced. And the decoupled models were reduced to first-order plus time delay models by analyzing the amplitude-frequency and phase-frequency characteristics. Secondly, according to the closed-loop characteristic equation of Smith predictor structure, PI controllers were designed following the principle of pole assignment for Butterworth filter. Finally, using small-gain theorem and Nyquist stability criterion, sufficient and necessary conditions for robust stability were analyzed with multiplicative uncertainties which encountered frequently in practice. The illustrative example was given to show the superiority of response speed and load disturbance rejection performance.

Robust stability of positive discrete-time linear systems of fractional order

Robust stability of positive discrete-time linear systems of fractional orderThe paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order - in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order - in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order - in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

Robust stability of positive continuous-time linear systems with delays

Robust stability of positive continuous-time linear systems with delaysThe paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

Robust Stability of Time-Varying Uncertain Systems With Rational Dependence on the Uncertainty

Robust stability of time-varying uncertain systems is a key problem in automatic control. This note considers the case of linear systems with rational dependence on an uncertain time-varying vector constrained in a polytope, which is typically addressed in the literature by using the linear fractional representation (LFR). A novel sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI) feasibility test by exploiting homogeneous polynomial Lyapunov functions, the square matrix representation and an extended version of Polya's theorem which considers structured matrix polynomials. It is shown that this condition is also necessary for second-order systems, and that this condition is less conservative than existing LMI conditions based on the LFR for any order.

Stability in the domain of nonlinear difference inclusions1

The problem of establishing the sufficient conditions for robust stability in a given domain is considered for the class of nonlinear discrete systems described by a difference inclusion. The nonlinear function of the system cannot be represented in a quasilinear form, and only nonlinear constraints are specified for its values. Examples of constructive testing of the sufficient stability conditions are presented.

Stability analysis of circuits including BJT differential pairs

In this paper, a necessary and sufficient condition for robust stability of electronic circuits at high frequency, which contain differential pair (emitter–coupled pair), is proposed. In fact, when emitter–coupled pairs are used as one input signal–one output signal, they have uncertainty in their transfer functions at high frequency. Even it is shown that this uncertainty can cause instability in closed loop electronic circuits at high frequency.The uncertainty is modeled as multiplicative perturbation in the transfer function of the differential pair at high frequency. Based on this uncertainty model, a necessary and sufficient condition for robust stability of above electronic circuits at high frequency is presented. This condition guarantees internal stability of the circuit at high frequency with respect to the uncertainty.

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.

Robust exponential stabilization for network-based switched control systems

It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A network-based switched control system, as a special case of networked control systems, is studied. Such a system is represented with network-induced delays and packet dropout as a switched delay system. Sufficient conditions for robust exponential stability are derived for a class of switching signals with average dwell time. A stabilization design for continuous-time, linear switched plant with nonlinear perturbation under a given communication network via a hybrid state feedback controller is proposed. A hybrid controller design is network-dependent and given in terms of linear matrix inequalities.

Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems

This work deals with the robust almost sure (AS) stabilization problem for continuous-time Markov jump linear systems (MJLS). Norm-bounded uncertainties affecting the system state and input matrices are considered. A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix. Such a condition can be profitably employed also to design a robust feedback stabilization strategy. Such feedback design is based on a formulation of the sufficient condition for robust AS stability in terms of an equivalent LMI problem.

An Improved Adaptive Control Algorithm Based Upon Unfalsified Control

In this paper, an improved algorithm for data-driven adaptive control that includes ideas from Unfalsified Control is presented. This work extends our previous work on suitable cost functions in Unfalsified Control and the use of optimization to improve the set of controllers by an additional sufficient condition for robust stability that is derived only from the measured data. This condition is also used to falsify controllers in order to avoid that a non-robust controller is put into the loop.

Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variational Inequalities

This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order variational analysis allowing us, in particular, to derive necessary and sufficient conditions for robust Lipschitzian stability of solution maps to parameterized variational inequalities with evaluating the exact bound of the corresponding Lipschitzian moduli. The efficient coderivative calculations and characterizations of robust stability obtained in this paper are the first results in the literature for the problems under consideration in infinite-dimensional spaces. Most of them are also new in finite dimensions.

Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay's inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.

Robust ℓp stability and robust ℓ∞ stabilization over a rate-limited digital channel

This paper is concerned with robust stabilization of an uncertain system over a rate-limited digital channel from the viewpoint of input-output stability. Because of the quantization in the communication channel, it is impossible to apply the traditional small gain theorem to establish robust stability of the feedback system. To overcome this difficulty, we introduce a new notion of small ℓp signal ℓp stability, and derive a sufficient robust stability condition against ℓp gain-bounded uncertainty based on this notion. Furthermore, for the case of p = ∞, a sufficient data rate for the existence of a robustly stabilizing encoder-controller pair is explicitly given.

Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization

In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF) method and can be applied to very general nonlinear time-varying systems with disturbance and control inputs, including both finite and infinite-dimensional systems. The generality of the proposed methodology is also reflected upon by the fact that partial stability with respect to output variables is addressed. In addition, it is shown that the generalized CLF method can lead to a novel tool for the explicit design of robust nonlinear controllers for a class of time-delay nonlinear systems with a triangular structure.