Robust Stability Analysis Method Research Articles

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 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 conditions for polytopic systems

The paper provides a survey of some recent robust stability conditions, their mutual comparisons, and presents new robust stability conditions for continuous- and discrete-time systems with convex polytopic uncertainty. Robust stability analysis is based on LMI conditions and parameter-dependent Lyapunov functions. The developed stability conditions are appropriate for output feedback design. Numerical examples thoroughly illustrate the power of the considered robust stability analysis methods and show which of them provides the less conservative results.

ROBUSTNESS ANALYSIS OF EXPONENTIAL TRACKING WITH DISTURBANCE ATTENUATION BY OUTPUT FEEDBACK (ETDAOF) WITH TIME DELAY IN THE PROCESS INPUT

ABSTRACT This article considers exponential tracking with disturbance attenuation by output feedback (ETDAOF) control for systems with time delay in the process input. It is shown that the stability of such systems can be analyzed through a small-gain theorem. This robust stability analysis method is helpful in making decisions in controller synthesis. The analysis method is used to synthesize an ETDAOF controller for a highly nonlinear pH neutralization process. Simulation results are presented.

Graphical and numerical approach to robust stability analysis of fuzzy modeled systems with parametric uncertainty and disturbance

In this paper, robust stability analysis methods for the fuzzy feedback control systems are presented, the graphical method via multivariable circle criterion and the numerical method via linear matrix inequalities (LMI). The well-known Takagi–Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties are assumed to be included in the model structure with known bounds. For these structured parametric uncertainties, L 2 robust stability analysis is performed by taking external disturbance as input and system state as output. The effectiveness of the proposed methods is illustrated by examples.

Biquadratic stability of uncertain linear systems

Deals with the problem of stability analysis for linear systems with uncertain real, possibly time-varying, parameters. A robust stability approach based on a Lyapunov function which depends quadratically on the uncertain parameters as well as in the system state is proposed. This robust stability approach, referred to as biquadratic stability, is suited to deal with uncertain real parameters with magnitude and rate of change which are confined to a given convex region. A linear matrix inequality based sufficient condition for biquadratic stability is developed. The proposed robust stability analysis method includes quadratic stability and affine quadratic stability as particular cases.

On stability criterion for H ∞ control systems including delayed perturbations

Abstract In this technical note, in the light of Razumikhin-type theorem, a delay-dependent stability criterion for H∞ control systems including uncertain time-delay perturbations is presented. Since our result is easily applicable, it may provide an effective method for robust stability analysis of H∞ control systems with delayed perturbations.

Design of robust direct adaptive controllers for SISO systems: Time and frequency domain design conditions

This paper presents the design of a robust direct model reference adaptive control (DMRAC) algorithm with focus on the satisfaction of an almost strictly positive real (ASPR) condition in the presence of plant uncertainty represented as either variations in plant parameters or unmodelled dynamics in the form of additive or multiplicative norm bounded perturbations in the transfer function. Both the time and frequency domain design conditions for a feedforward compensator have been developed utilizing the robust stability analysis and optimization methods. Illustrative examples are presented to validate the algorithm's use and applicability to control systems with parametric uncertainty or unmodelled dynamics.

Robust stability analysis and design method for the fuzzy feedback linearization regulator

A robust stability analysis and design method for a fuzzy feedback linearization regulator is presented. The well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. Also, based on the stability analysis, a systematic design procedure for the fuzzy feedback linearization regulator is provided. The effectiveness of the proposed analysis and design method is illustrated by a simple example.

Stability criterion for LQ regulators including delayed perturbations

In this technical note, in the light of Razumikhin-type theorems, a delay-dependent stability criterion for LQ regulators including uncertain time-delay perturbations is presented. Since our result is easily applicable, it may provide an effective method for robust stability analysis of LQ regulators with delayed perturbations.

Criteria for Robust Stability of Uncertain Linear Systems with Time-Varying State Delays

This paper deals with the problem of robust stability analysis for a class of uncertain linear systems with time-varying state delays. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state space model. We develop a delay-dependent method for robust stability analysis. The proposed method is given in terms of linear matrix inequalities.