Robustness of reduced‐order observer‐based feedback control for discrete two‐time‐scale systems

Abstract

A design method to achieve robust stability and performance criteria for discrete two‐time‐scale systems controlled by low‐order observer‐based compensators is proposed. Sufficient conditions for stability and performance robustness are established by an easy extension of the small gain theorem. The theoretical analysis is illustrated by a numerical example.     

Robust pole‐assignment for dynamic systems with uncertain parameters

Abstract

In this paper, by using discrete‐type Lyapunov stability criterion, new sufficient conditions for robust pole‐assignment of uncertain systems in a specified disk are presented. The norm bound on linear time‐invariant perturbations is obtained. The relationship between the allowable bound and the eigenvalues of the nominal system matrix is discussed. A design method for robust pole‐assignment is proposed. Examples are given to demonstrate the use of the proposed techniques.     

Robust stability analysis for linear uncertain time‐delay systems with delay‐dependence

Abstract

This paper proposes a sufficient robust stability condition for uncertain time‐delay systems with delay‐dependence. The results obtained include information on the delay time and is less conservative than delay‐independent results which have been published when delays are small. Examples are given to illustrate the application of our results.     

Decentralized robust control of multi‐machine power systems with a prescribed degree of stability

Abstract

This paper presents a completely decentralized scheme for the robust control of multi‐machine power systems with a prescribed degree of stability. By applying the optimal control technique to the nominal dynamics of each decomposed machine, the calculated optimal gains are multiplied by appropriate factors to account for the intrinsic uncertainties and nonlinear interactions among the machines. This subsystem‐based method can give the overall system an arbitrarily chosen degree of stability, where no state information is transferred. An example of a three‐machine power system is given below.     

On the robust stability for continuous large‐scale uncertain systems with time delays in interconnections

Abstract

In this paper, the robust stability testing problem is addressed for continuous large‐scale uncertain systems with time delays in interconnections. Three classes of system uncertainties are examined: (i) nonlinear time‐varying uncertainties; (ii) linear unstructured uncertainties; and (iii) linear highly structured uncertainties. By applying the Lyapunov stability theorem, several new delay‐independent sufficient conditions are established in terms of concise inequalities, which can maintain the stability of continuous large‐scale uncertain time‐delay systems. Finally, illustrative examples are given to demonstrate the application of the results presented here.     

Genetic robust controller design for uncertain systems with time‐delays in both state and control input via LMI approach

Abstract

In this paper, the robust control for uncertain delay systems in state and control input is considered. The uncertainty is nonlinear time‐varying perturbations and does not require a matching condition but is norm‐bounded. Based on the constructive use of Lyapunov functional, delay‐dependent stabilizability criteria are proposed to guarantee stability for the systems via linear control. Linear matrix inequality (LMI) and Genetic algorithms are used to design a memoryless state‐feedback controller. Two numerical examples are given to illustrate that the proposed results are less conservative than some others.     

Robust H 8 output feedback control for general nonlinear systems with structured uncertainty

Abstract

In this paper, the robust H ⁸ output feedback control problem for general nonlinear systems with L ₂‐norm‐bounded structured uncertainties is considered. Sufficient conditions for the solvability of robust performance synthesis problems are represented in terms of two Hamilton‐Jacobi inequalities with n independent variables. Based on these conditions, a state space characterization of a robust H ⁸ output feedback controller solving the considered problem is proposed. An example is provided for illustration.     

Robust pole assignment for interval polynomial based on positive interval Routh-table: positive property of Routh-table of binomial coefficients

This paper elucidates a robust pole assignment (RPA) scheme for an interval polynomial based on positive interval Routh-table using a binomial coefficients feedback gain. The robust scheme transforms the problem of RPA into the problem of solving a family of stability condition polynomials that have positive function values. The condition for the existence of solution is that all entries of the Routh-table of binomial coefficients (RTBC) are positive. Importantly, this paper provides an advanced general formula for the generated entries of the RTBC, confirming that all entries of RTBC are positive. An illustrative example reveals the effectiveness of the scheme.     

Allowable perturbations for the stability robustness of systems with uncertain parameters

Abstract

This paper presents new techniques to analyze the stability robustness of linear time‐invariant systems in state space models. The fundamental criteria derived before for testing the stability robustness of autonomous systems are applied to the robustness analysis of multivariable feedback systems. Both the norm bound and the element bound for allowable perturbations are obtained. A stability robustness index is defined which is useful both for the analysis and the synthesis of control systems.     

LQR/RPS design of robust controllers for a one‐link robot

Abstract

In this paper, a design method for robust controllers for a one‐link robot is developed. Based on a linearized model of this nonlinear robot system, the linear quadratic regulator (LQR) design method is incorporated with a reduced parameter sensitivity (RPS) technique to design a robust proportional‐plus‐integral (PI) controller to achieve better performance in position control. This robust controller can tolerate real parameter variations resulting from the mechanical loads of applications. A direction method is further developed and used to evaluate the stability robustness of this controlled system. Combining the direction method with the LQR/RPS method, a robust PI controller can be generated to avoid improper over‐design. Both computer simulation and experimental results demonstrate the feasibility and effectiveness of the proposed approach.     

Pole‐assignment of dynamic interval systems

Abstract

A simple sufficient condition which guarantees that all the eigenvalues of an interval matrix will lie inside a circle centered at α with radius r is formulated. A design procedure of robust state feedback controllers for dynamic interval systems is demonstrated by an example.     

Stability criteria for neutral systems with time‐varying delays and nonlinear uncertainties

Abstract

The asymptotic stability problem for a class of neutral systems with time‐varying delays and nonlinear uncertainties is investigated in this paper. LMI‐based delay‐dependent criteria are proposed to guarantee the asymptotic stability of the considered systems. New Lyapunov‐Krasovskii functional and Leibniz‐Newton formulae are used to find the delay‐dependent stability results. Finally, some numerical examples are illustrated to show the improved results from using this method.     

On the stability of uncertain homogeneous bilinear systems subjected to time‐delay and constrained inputs

Abstract

This paper addresses the stability test problem for homogeneous bilinear uncertain time‐delay systems with constrained inputs. By using differential inequality, some sufficient criteria are presented to guarantee the asymptotic stability of overall systems. Furthermore, the transient behaviors of the mentioned systems are also estimated.     

DESIGN OPTIMIZATION FOR ROBUSTNESS USING QUADRATURE FACTORIAL MODELS

Abstract

This paper describes a robust optimization methodology for designs involving either complex simulations or actual experiments. The methodology adopts a new objective function that consists of the Expected Performance (EP) and the weighted Deviation Index (DI). The proposed Quadrature Factorial Model estimates the expected performance and the standard deviation of a design. This scheme greatly reduces the number of experiments and provides superior results for systems with significant interaction effects and nonlinear variations. The proposed methodology is applied to the design of helical gears with minimum transmission error. The robust optimum shows a significant reduction of the expected transmission error compared with previous studies, while maintaining the insensitivity to manufacturing errors and load variation.     

Robust stability for perturbed discrete systems with time delay

Abstract

In this paper, we present a roubust stability condition for linear perturbed discrete time‐delay systems. The perturbations are treated with highly structured information. A state feedback controller for the aforementioned systems is also introduced. Examples are given to demonstrate the result.     

Delay‐dependent H∞ observer‐based control for uncertain neutral systems via LMI optimization approach

Abstract

In this paper, the delay‐dependent H∞ observer‐based control for a class of uncertain neutral systems with time‐varying delays is considered. The linear matrix inequality (LMI) optimization approach is used to design the H∞ robust control with disturbance attenuation. The control and observer gains are given from the LMI feasible solutions. Some numerical examples are given to illustrate the use of the main result.     

Stability and robustness of time‐delay systems

Abstract

Using some properties of matrix measures and matrix's spectral radius, a new stability criterion for a linear time‐delay system is derived. This result is also extended to interval time‐delay systems.     

Stability of schur polynomials under coefficient perturbation

Abstract

In this paper, we are concerned with the stability robustness of characteristic polynomials with perturbed coefficients for linear discrete‐time systems. An upper bound on the allowable coefficient perturbation of a Schur polynomial with retaining stability is obtained. The proposed upper bound is directly formulated in terms of the polynomial under consideration and its value can be determined by numerical computation. We also provide a sufficient condition for the stability of interval polynomials.     

Counteracting quantum decoherence with optimized disorder in discrete-time quantum walks

ABSTRACT

Decoherence and disorder are two major difficulties limiting the performance of quantum systems in practical settings. Yet they can potentially counteract each other to partially restore the systems' quantum signatures. We adopt the particle swarm optimization method to find the optimal disorder for mitigating the effects of decoherence in one- and two-dimensional quantum random walks, achieving substantial increase in the mean walking distance for a wide range of decoherence strength. This result suggests a viable approach to constructing practical quantum systems robust against decoherence and disorder.     

Fuzzy controllers for nonlinear interconnected tmd systems with external force

Abstract

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and active fuzzy controllers in reducing structural responses under external forces. In general, TMD is good for linear systems. We propose here a fuzzy controller to deal with nonlinear systems. For the fuzzy controller, a stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of interconnected TMD systems. Based on decentralized control and this criterion, a set of model‐based fuzzy controllers are then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected TMD system. Finally, an example is given to illustrate the concepts discussed throughout this paper.