Time-varying Structured Uncertainties Research Articles

Criteria for Stability and Stabilization of Variable Fractional-Order Uncertain Neutral Systems With Time-Varying Delay: Delay-Dependent Analysis

This work focuses on the stability and stabilization of variable fractional-order neutral systems (VFONS) with time-varying delays and time-varying structured uncertainties. Via the FO Lyapunov function, a new set of delay-and order-dependent criterion is proposed for both nominal and uncertain VFONS. The resultant criteria are formulated by designing a linear matrix inequality-based static output feedback control strategy in a set of linear matrix inequalities. The numerical simulations verify the theoretical formulation.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay.

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L2 -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L2 -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper investigates the problem of robust stability for neutral type system with mixed delays and time-varying structured uncertainties. Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method, some new stability criteria are presented. The difference between this paper and other existing results is that the lower bounds and upper bounds of the neutral-delay and discrete-delay are considered, which will obtain some less conservative stability analysis results. Several numerical examples are given to demonstrate the effectiveness and merit of the proposed results.

Novel passivity criteria for neural networks with discrete and unbounded distributed time-varying delays

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria.

On Stability of Neutral Systems with Time-Varying Delay

This paper investigates the delay-dependent robust stability of neutral systems with time-varying discrete delays and time-varying structured uncertainties. New delay-dependent stability criteria are obtained and formulated in the form of a linear matrix inequality. Since the criteria take the sizes of the neutral delay, discrete delay and derivative of discrete delay into account, they are less conservative than previous methods. Numerical example is given to indicate significant improvements over some existing results.

Robust passivity analysis for Takagi–Sugeno fuzzy stochastic Cohen–Grossberg interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic Cohen–Grossberg fuzzy interval neural networks with time-varying delays. Two types of uncertainties, time-varying structured uncertainty and interval uncertainty, are considered. By constructing proper Lyapunov–Krasovskii functionals and utilizing the stochastic analysis technique, some delay-dependent passivity conditions are derived to ensure the passivity of the concerned neural networks. The proposed results can be expressed in terms of linear matrix inequalities, which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits of the proposed method.

A less conservative robust stability criteria for uncertain neutral systems with mixed delays

This paper is concerned with the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. By considering the cross-terms with additional design parameters, a complete form of Lyapunov–Krasovskii functional is constructed. Then some free weighting matrices are introduced, and a sufficient stability condition is obtained in terms of linear matrix inequalities. The obtained criterion is dependent on the sizes of neutral delay and discrete delay and are less conservative than those produced by previous approaches. Numerical examples are given to illustrate both the improvement the proposed method provides over some existing ones and the relationship between the neutral- and discrete-delay.

New delay-dependent conditions on robust stability and stabilisation for discrete-time systems with time-delay

This article is concerned with new robust stability conditions and robust stabilisation method for a discrete-time system with time-delay and time-varying structured uncertainties that come into state and input matrices. An improved approach to obtain new robust stability conditions is proposed. Our approach employs a generalised Lyapunov functional combined with the parameterised model transformation method and the generalised free weighting matrix method. These generalisations lead to generalised robust stability conditions that are given in terms of linear matrix inequalities. Moreover, based on new robust stability conditions, a robust stabilisation method for uncertain discrete-time systems with time-delay is given. Numerical examples compare our robust stability conditions with some existing conditions to show the effectiveness of our approach and also illustrate the improvement of our robust stabilisation method.

Novel delay-dependent robust stability criteria for uncertain neutral systems with time-varying delay

The problem of delay-dependent robust stability for neutral control systems with time-varying delay and time-varying structured uncertainties is investigated. An improved linear matrix inequality-based delay-dependent stability test is introduced to ensure a large upper bound for time-delay. A new class of Lyapunov–Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coefficient matrix is constructed to derive some novel delay-dependent stability criteria. Finally, numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

This paper investigates the stability robustness of linear output feedback systems with both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties as well as delayed perturbations by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, two new sufficient conditions are proposed for ensuring that the linear output feedback systems with delayed perturbations as well as both time-varying structured and unstructured parameter uncertainties are asymptotically stable. The corresponding stable region, that is obtained by using the proposed sufficient conditions, in the parameter space is not necessarily symmetric with respect to the origin of the parameter space. Two numerical examples are given to illustrate the application of the presented sufficient conditions, and for the case of only considering both the delayed perturbations and time-varying structured parameter uncertainties, it can be shown that the results proposed in this paper are better than the existing one reported in the literature.

Delay-dependent robust stability for neutral systems with mixed discrete-and-neutrai delays

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases. A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.

Convex Necessary and Sufficient Conditions for Frequency Domain Model (In)Validation Under SLTV Structured Uncertainty

This paper deals with the problem of model (in)validation of discrete time, causal, linear time-invariant (LTI) stable models subject to slowly linear time-varying structured uncertainty, using frequency domain data corrupted by additive noise. It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks. The main contribution of this paper shows that, on the other hand, if one considers arbitrarily slowly time varying uncertainty and noise in L/sub 2/, then tractable, convex necessary and sufficient conditions for (in)validation can be obtained. Additional results include a discussion of the case where the noise is characterized in terms of the L/sub /spl infin// norm.

Robust stability for delay Lur'e control systems with multiple nonlinearities

This paper deals with delay Lur'e control systems with multiple nonlinearities and time-varying structured uncertainties. First, some sufficient, and necessary and sufficient conditions for the existence of a Lyapunov functional in the extended Lur'e form with a negative definite derivative that guarantees delay-independent robust absolute stability are presented. Then, some new less conservative delay-dependent absolute stability criteria are derived that employ free weighting matrices to express the relationships between the terms in the Leibniz–Newton formula. All the criteria are based on linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the method.

Regional eigenvalue-clustering robustness of linear output feedback systems with both time-varying structured and unstructured uncertainties as well as nonlinear actuators

This paper investigates the regional eigenvalue‐clustering robustness of linear output feedback systems with both time‐varying structured (elemental) and unstructured (norm‐bounded) parameter uncertainties as well as nonlinear actuators. A sufficient condition is proposed for ensuring that all the eigenvalues of output feedback systems with both time‐varying structured and unstructured parameter uncertainties as well as nonlinear actuators remain inside the specified region. No restriction is imposed on the shapes of the specified region. The proposed method is applicable to both the continuous‐time case and the discrete‐time case. When all the eigenvalues are just required to locate in the stable region, the proposed criterion will become the stability robustness criterion. Two numerical examples are given to illustrate the application of the proposed sufficient condition.

Stability robustness of linear output feedback systems with both time-varying structured and unstructured uncertainties as well as actuator saturation

Stability robustness of linear output feedback systems with both time-varying structured and unstructured uncertainties as well as actuator saturation

Stability robustness of linear output feedback systems with both time-varying structured and unstructured uncertainties as well as actuator saturation

This paper investigates the stability robustness of linear output feedback systems with actuator saturation as well as both time-varying structured (elemental) and unstructured (norm-bounded) parameter uncertainties by directly considering the mixed quadratically coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the linear output feedback systems with actuator saturation as well as both time-varying structured and unstructured parameter uncertainties are robustly stable. A numerical example is given to illustrate the application of the presented sufficient condition.

Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper concerns the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. A new method based on linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds on the delays and the free weighting matrices. Since the criteria take the sizes of the neutral- and discrete-delays into account, it is less conservative than previous methods. Numerical examples illustrate both the improvement this approach provides over previous methods and the reciprocal influences between the neutral- and discrete-delays.

Robust Stability of Linear Continuous/Discrete-Time Output Feedback Systems with Both Time-Varying Structured and Unstructured Uncertainties

This paper investigates the stability robustness of linear continuous/discrete-time systems with output feedback controllers as well as both time-varying structured and unstructured parameter uncertainties by directly considering the mixed quadratically-coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, some new sufficient conditions are proposed for ensuring that the linear output feedback systems with both time-varying structured and unstructured parameter uncertainties are asymptotically stable. Three numerical examples for continuous-time and discrete-time systems are given to illustrate the application of the presented sufficient conditions, and for the case of only considering time-varying structured parameter uncertainties, the proposed sufficient conditions are shown to be less conservative than the existing ones reported in the literature.

Sufficient conditions for the controllability of linear descriptor systems with both time-varying structured and unstructured parameter uncertainties

In this paper, under assumptions that the linear nominal descriptor system is regular and controllable, some sufficient conditions are proposed to preserve the assumed properties when both time‐varying structured and unstructured parameter uncertainties are added into the nominal descriptor system. The corresponding results for the dual observability robustness problems are straightforward extensions. It is shown that the proposed sufficient conditions are the generalized versions of the results reported recently in the literature.

Robust H 2 control of descriptor system with time-varying uncertainty

For a descriptor system with time-varying structured uncertainty, this paper considers the robust H 2 control problem of finding a controller satisfying the prescribed H 2 performance level against all possible uncertainty under the constraint of robust stability. A sufficient condition for the robust H2 performance is derived in terms of a linear matrix inequality (LMI). Based on this LMI condition, we develop a design method of a descriptor variable feedback controller achieving the robust performance. The present design method can solve the robust H 2 control problem for a wider class of plants than the state-space approach. A numerical example is also included to show the applicability of the present method.