Sufficient Conditions For Robust Stability Research Articles

Robust decentralized control of perturbed fractional-order linear interconnected systems

The robust decentralized state feedback stabilization problem for a class of perturbed fractional-order linear interconnected systems is investigated. The systems considered are subject to structured or unstructured perturbations. The decentralized state feedback controllers are designed such that the closed-loop perturbed fractional-order linear interconnected systems are asymptotically stable. By using the definition of positive and negative definite matrices and stability theory of fractional-order systems, sufficient conditions for robust stabilization of closed-loop perturbed fractional-order linear interconnected systems are given. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.

Research on Robust Control of Gas Tungsten arc Welding System with the LMI Approach

By using the Lyapunov second method, the robust control and robust optimal control for the gas tungsten arc welding dynamic process whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain. As results, 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 and controlling variable welding speed, is worked out to illustrate the proposed results. It is shown in the paper that the sampling period is the crucial design parameter

Global Robust Exponential Stability for Interval Delayed Neural Networks with Possibly Unbounded Activation Functions

In this paper, we mainly study the global robust exponential stability of the neural networks with possibly unbounded activation functions. Based on the topological degree theory and Lyapunov functional method, we provide some new sufficient conditions for the global robust exponential stability. Under these conditions, we prove existence, uniqueness and global robust exponential stability of equilibrium point. In the end, some examples are provided to demonstrate the validity of the theoretical results.

Unfragile Passive Control of Uncertain Sampling System

The unfragile passive control problem of a class of uncertain state-delay sampling system is discussed. Applying Lyapunov method, and combining the properties of matrix inequality, the sufficient condition of robust stability is given, and the unfragile passive controller is designed. Finally a numerical example illustrates the effectiveness and the availability for the design. Index Terms - Uncertain State-delay Sampling System , Linear Matrix Inequility , Unfragile Passive Control .

Sufficient and Necessary LMI Conditions for Robust Stability of Rationally Time-Varying Uncertain Systems

This technical note addresses robust stability of uncertain systems with rational dependence on unknown time-varying parameters constrained in a polytope. First, the technical note proves that a sufficient linear matrix inequality (LMI) condition that we previously proposed, based on homogeneous polynomial Lyapunov functions (HPLFs) and on the introduction of an extended version of Polya's theorem, is also necessary. Second, the technical note proposes a new sufficient and necessary LMI condition by exploiting properties of the simplex and sum-of-squares (SOS) parameter-dependent polynomials. Lastly, the technical note investigates relationships among these conditions and conditions based on the linear fractional representation (LFR). It is worth remarking that sufficient and necessary LMI conditions for this problem have not been proposed yet in the literature.

Asymptotic stability and stabilisation of uncertain delta operator systems with time‐varying delays

This study focuses on the asymptotic stability and stabilisation of uncertain linear systems with time-varying delays via delta operator approach. By employing a new model formulation, the time-delayed delta operator system is transformed into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation of delayed state and scaled small gain theorem, new delay-dependent sufficient conditions of robust asymptotic stability and state-feedback stabilisation of an uncertain delta operator time-delayed system are established by using a novel Lyapunov-Krasovskii functional. The criteria obtained unify some previously suggested relevant methods seen in literature for achieving asymptotic stability and stabilisation of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed methods.

A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks

The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.

Delay-dependent robust $$H_\infty $$ control for 2-D discrete nonlinear systems with state delays

This paper investigates the problem of robust $$H_\infty $$ control for a class of 2-D (two-dimensional) discrete state delayed systems with sector nonlinearity described by a model of Roesser type. Firstly, a delay-dependent sufficient condition of robust exponential stability for such 2-D discrete systems is derived in linear matrix inequalities (LMIs) form. Secondly, a delay-dependent exponential stability criterion with $$H_\infty $$ performance for the considered systems is also proposed. Then a state feedback $$H_\infty $$ controller is constructed based on the above results. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

Abstract This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.

Dynamic robust stabilization of stochastic differential control systems

The stabilization of stochastic differential control systems by means of dynamic feedback laws is provided. We extend the well-known Artstein–Sontag theorem to derive the necessary and sufficient conditions for the dynamic robust stabilization of stochastic differential systems. An explicit formula for feedback law exhibiting dynamic robust stability in probability is established, and a numerical example is also given to illustrate our results.

Robust stability analysis of Markov jump standard genetic regulatory networks with mixed time delays and uncertainties

This paper concerns the robust stability analysis problems for a class of nonlinear Markov jump standard genetic regulatory networks with mixed time-varying delays and parameter uncertainties. The standard genetic regulatory networks model is constructed via recurrent neural networks. The nonlinear regulatory function is assumed to satisfy the sector condition, and each regulatory function in the model has its own expression form. The mixed delays mean that the discrete delays and distributed delays are considered simultaneously. Based on linear matrix inequality techniques, sufficient conditions for robust stability of the underlying systems are first derived by using the conventional approach in the area of time-delay systems. Also, the “delay decomposition” approach is further utilized so as to improve the analytical results. Two numerical examples are exploited to verify the obtained theoretical findings.

New sufficient conditions for robust stability analysis of interval matrices

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using the proposed conditions are demonstrated through application to previous examples in the literature.

Robust Stability of a Multi-Agent System Under Arbitrary and Time-Varying Communication Topologies and Communication Delays

This technical note considers formation control of a group of identical agents that can communicate with each other. A necessary and sufficient condition for robust stability in the case of arbitrary time-invariant communication topologies and sufficient conditions in the case of arbitrary time-varying topology and communication delays are derived, that reduce the stability analysis and controller design problems to analysis or synthesis, respectively, for a single agent.

Robust stability analysis for an enhanced ILC-based PI controller

A novel combination of PI control and iterative learning control (ILC), referred to enhanced ILC-based PI control, was proposed in this study. This algorithm could be used on a class of multi-input multi-output batch processes with modeling uncertainties and unknown disturbances. Based on a two-dimensional (2D) Roesser's system description, a sufficient condition for robust asymptotical stability of the closed-loop system was derived in this paper. Furthermore, the monotonic convergence of the closed-loop system in the batch direction has been proved. Applications on a three-tank system show that the proposed method can achieve the design objective well, with performance improvement along both time and batch direction, and also owns good robustness to uncertainties and non-repetitive disturbances.

Robust stability and stabilization of uncertain switched discrete-time systems

This paper is concerned with the robust stability and stabilization 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 and stabilization 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 and stabilization 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.

DELAY-DEPENDENT ROBUST STABILIZATION AND H&#8734 CONTROL FOR UNCERTAIN STOCHASTIC T-S FUZZY SYSTEMS WITH MULTIPLE TIME DELAYS

In this paper, the problems of robust stabilization and H1 control for uncertain stochastic systems with multiple time delays represented by the Takagi-Sugeno (T-S) fuzzy model have been studied. By constructing a new Lyapunov-Krasovskii functional (LKF) and using the bounding techniques, sufficient conditions for the delay-dependent robust stabilization and H1 con- trol scheme are presented in terms of linear matrix inequalities (LMIs). By solving these LMIs, a desired fuzzy controller can be obtained which can be easily calculated by Matlab LMI control toolbox. Finally, a numerical simula- tion is given to illustrate the effectiveness of the proposed method.

A Matrix Technique for Dominant Pole Placement of Discrete-Time Time-Delayed Systems

A matrix method is introduced for determination of robust-stability zones of the general linear time invariant discrete-time dynamics with large delays against parametric uncertainties. The technique employs Kronecker Product and unique properties of palindrome polynomials. These polynomials are subset of self-inversive polynomials which exert advantageous tools for examination of the distribution of its zeros. The main motivation in this paper is to develop a practical tool for determination of robust stability zones against parametric uncertainties and dominant pole assignment in discrete-time domain. A sufficient condition for robust stability and dominant pole assignment is presented. The procedure for the solution is demonstrated via some example case studies.

Robust stability of systems of linear differential equations with periodic impulsive influence

We give sufficient robust stability conditions for matrix polytopes of linear systems with impulsive influence. The methods of our study are based on logarithmic matrix measure theory and linear operator theory in Banach spaces. Our results reduce the robust stability problem to the feasibility problem for a system of linear matrix inequalities in the class of positive definite matrices.

Stochastic exponential robust stability of interval neural networks with reaction–diffusion terms and mixed delays

The stochastic exponential robust stability is considered for a class of delayed neural networks with reaction–diffusion terms and Markov jumping parameters in this paper. It is assumed that the uncertain weight matrices belong to the given interval matrices. Some sufficient conditions for the stochastic exponential robust stability of the system are established by applying vector Lyapunov function method and M-matrix theory. The obtained results involving the effect of reaction–diffusion improve the existing conditions. Finally, two examples with numerical simulations are given to illustrate the obtained results.

Robust stability for fractional-order systems with structured and unstructured uncertainties

The issues of robust stability for uncertain fractional-order systems of two types of order α∈(0,1) are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition for robust stability is given; for the norm-bounded uncertainty case, a sufficient and necessary condition for robust stability is presented. Both of these conditions can be checked by solving sets of linear matrix inequalities. Two numerical examples are presented to confirm the proposed conditions.