Stability robustness analysis of discrete linear systems

The stability robustness of a discrete linear time-invariant system is analysed. Based on a discrete Lyapunov stability approach, fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems. The element bounds for the allowed perturbations are presented.     

Robust stability of discrete-time systems under parametricperturbations

Stability robustness analysis of a system under parametric perturbations is concerned with characterizing a region in the parameter space in which the system remains stable. In this paper, two methods are presented to estimate the stability robustness region of a linear, time-invariant, discrete-time system under multiparameter additive perturbations. An inherent difficulty, which originates from the nonlinear appearance of the perturbation parameters in the inequalities defining the robustness region, is resolved by transforming the problem to stability of a higher order continuous-time system. This allows for application of the available results on stability robustness of continuous-time systems to discrete-time systems. The results are also applied to stability analysis of discrete-time interconnected systems, where the interconnections are treated as perturbations on decoupled stable subsystems     

Robust absolutely stable Lurie systems

This paper considers the robustness of Lurie systems with multiple non-linearities subject to modelling uncertainties and large parameter variations in the system dynamics. New robustness results on Lurie systems are presented which lead to a reduction of conservatism in robustness tests of absolute stability. It is shown that if the perturbations lie along given directions, it is possible to calculate a sector such that the perturbations belonging to the given direction do not disturb system stability. The proposed approaches for robustness analysis are based on the Popov frequency domain criterion as well as on the algebraic criterion for the absolute stability. The robustness results are illustrated by a second-order numerical example.     

New robustness bounds for discrete systems with randomperturbations

Some new stochastic stability robustness bounds for state-space models are reported. Nominally exponentially stable discrete-time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness. The methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one. The results are compared with each other and with the exact stability region in an example     

Robust control of a class of sampled-data systems with LTI uncertainties

The robust stability and robust performance in sampled-data control is studied for systems with LTI uncertainties. A class of problems is considered, which allows an exact characterization of robust stability of the sampled-data system in terms of the _H norm of a finite-dimensional discrete transfer function. In the problem class certain assumptions on the product of the uncertainty weight and the anti-aliasing prefilter are imposed. In return, the robustness conditions can be stated in a particularly compact form, in which the robust stability and performance problems for LTI perturbations reduce to standard finite-dimensional discrete robust stability and performance problems. The robust stability condition for LTI uncertainties is also compared to the robustness condition based on the small gain theorem. The analysis provides a method to estimate the conservatism of the small gain robustness condition directly in terms of the anti-aliasing prefilter and frequency weights. As a by-product of this analysis a non-trivial class of sampled-data systems is identified for which the small gain theorem gives a non-conservative condition for robust stability to norm-bounded LTI uncertainties.     

Structured singular value analysis of multidimensional systemstability

Structured singular value computations are being developed for analysis of robustness of multivariable control systems. It is shown that the same computational tools can be used to test the stability of multidimensional systems     

Robustness of pole-assignment in a specified region

An analysis of pole-assignment is given for systems under linear time-invariant perturbations. Based upon the Lyapunov approach, new techniques to calculate allowable element bounds for highly structured perturbations are presented. Under these allowable perturbations both stability robustness and a certain performance robustness are thus ensured. Examples are given to illustrate the proposed methods     

On robustness of Lurie systems with multiple non-linearities

The robustness of absolute stability of Lurie systems with multiple non-linearities, with respect to model variations, is considered. Two approaches for robustness analysis are developed. One is based on the Popov frequency domain criterion and the other on the algebraic criterion for the absolute stability. It is shown that there exist finite perturbations in the system model which admit certain norm bounds so that the stability of the system is not affected. Computationally, the method is very feasible; it involves a very simple numerical algorithm. Two illustrative examples are worked out. The theory is applied to characterize the robustness properties of a steam boiler example of a Yugoslav thermal power plant.     

Robustness analysis and synthesis of SISO systems under both plant and controller perturbations

In this paper, we consider the robustness analysis and synthesis problem for a class of control systems under both plant and controller perturbations. Necessary and sufficient conditions are given for robust stability of SISO systems subject to additive norm-bounded perturbations. Linear matrix inequality (LMI)-based controller design method is presented. Robust stability of systems with both plant and controller perturbations, and stability analysis of a class of multilinear disc polynomials are unified in the same framework, and can be solved by computing the largest norm of a second-order matrix along the imaginary axis.     

Robustness analysis of nonlinear feedback systems: an input-outputapproach

This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection     

Robustness analysis of uncertain linear singular systems withoutput feedback control

The robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered. The problem is transformed into a robust nonsingularity problem. Based on the linear fractional transformation (LFT) approach, the robustness bounds to preserve regularity, impulse immunity, and stability are found in terms of the structured singular value μ with respect to parametric uncertainties. The LFT approach provides a unified framework for robustness analysis of both uncertain linear continuous/discrete-time singular systems     

Stability of Networked Control Systems Under a Multiple-Packet Transmission Policy

This paper is concerned with stability analysis of discrete-time networked control systems subject to packet loss under a multiple-packet transmission policy with the packet dropping probability of the communication channel bounded from above. Necessary and sufficient conditions for stability are obtained. In addition, the packet dropping margin as a measure of stability robustness of a system against packet loss is defined and its formula is derived. A design method is proposed for enhancing stability robustness subject to the constraint of a set of prescribed nominal closed-loop poles.      

On robust stabilizability of linear differential-difference systemswith unstable D-operator

The robustness of linear delayed neutral-type control systems with the unstable difference operator is considered. The robustness analysis is stipulated by the impossibility of implementing precisely derivative feedback. Different approximations of stabilizing controls and their influence on the stability of the closed-loop system are considered     

A fundamental multivariable robustness theorem for robusteigenvalue assignment

A fundamental robustness theorem for robust eigenvalue assignment of multivariable feedback systems is derived. The theorem determines whether a perturbed multivariable feedback system has its characteristic polynomial zeros located in the same regions as the nominal system does. It can be applied to continuous systems as well as to discrete systems. The theorem can handle nonsquare transfer matrices as well as dynamic output feedback. Conditions are discussed under which the proposed theorem reduces to a fundamental theorem for stability robustness analysis     

Stable and robust fuzzy control for uncertain nonlinear systems

Presents the stability and robustness analysis for multivariable fuzzy control systems subject to parameter uncertainties based on a single-grid-point (SGP) approach. To perform the analysis, we represent a multivariable nonlinear system using a TS-fuzzy plant model. Three design approaches of fuzzy controllers are introduced to close the feedback loop. By estimating the matrix measures of the system parameters and parameter uncertainties, stability and robustness conditions for different cases are derived. Application examples are given to show the design procedures and the merits of the proposed fuzzy controller     

Expansion of det(A+B+C) and robustness analysis of discrete-timestate-space systems

In this paper, the expansion of det(A+B+C) is given. The robustness problem for discrete-time state-space systems with uncertain parameters is investigated by applying the Schur stability theory of interval polynomials. A stability robustness criterion for the uncertain systems is derived. Illustrative examples are presented     

基于LMI的非线性摄动系统鲁棒绝对稳定性判据

讨论了前馈通道同时存在对象和控制器的范数摄动,而反馈通道存在扇区非线性的摄 动系统的稳定性问题.基于H∞理论和LMI方法,得到了一组由线性矩阵不等式表达的充分性 条件,建立了判断非线性摄动系统鲁棒绝对稳定性的新判据.     

Improved bounds for linear discrete-time systems with structuredperturbations

A time-domain analysis of the stability robustness of linear discrete-time systems subject to time-varying structured perturbations is considered. The Lyapunov stability theory is used to obtain bounds on the perturbation such that the systems remain stable. It is shown that these bounds are less conservative than the existing ones. This is illustrated via two numerical examples     

Model algorithmic control (MAC); basic theoretical properties

A mathematical framework for the analysis of model algorithmic control is developed and the operations of the main components of the control structure are described. The single input-single output case is treated in detail and results pertaining to the stability and the robustness of such systems are derived, both for deterministic and stochastic (colored output additive noise) environment. The case of the nonminimum phase plant is also considered. The robustness problem is discussed and performance ‘measures’ of robustness are proposed. The results derived in this paper are more generally applicable to optimizing type of control laws. In particular, the paper establishes a close link between the stability and closed loop properties of optimizing type and feedback type of control laws.     

Observer-based strict positive real (SPR) feedback control system design

This paper presents theory for stability analysis and design for a class of observer-based feedback control systems. Relaxation of the controllability and observability conditions imposed in the Yakubovich-Kalman-Popov (YKP) lemma can be made for a class of nonlinear systems described by a linear time-invariant system (LTI) with a feedback-connected cone-bounded nonlinear element. It is shown how a circle-criterion approach can be used to design an observer-based state feedback control which yields a closed-loop system with specified robustness characteristics. The approach is relevant for design with preservation of stability when a cone-bounded nonlinearity is introduced in the feedback loop. Important applications are to be found in nonlinear control with high robustness requirements.