Linear systems with a polynomial uncertainty structure: Stability margins and control

Microgrids are gaining considerable attention due to the installation of renewable power generation resources in areas that are closer to the load centers. The multivariable droop idea, acknowledges active power sharing by concurrent drooping of both voltage and frequency, in resistance as well as weak grids. To develop a multivariable-droop synchronous current converter control strategy for current management using Lyapunov stability of microgrid applications. In this paper overview of Lyapunov stability of linear continuous systems is presented. The conditions for the existence of the solutions for both regular and irregular singular linear systems are introduced. To guarantee an asymptotical stability for linear continuous singular systems and new stability conditions are analyzed. A considerable attention is focused on the design of controllers for multivariable linear systems so that certain system properties could be preserved under various classes of perturbations occurring in the system. It presents a multivariable-droop synchronous current converter control strategy for current management of weak grid/microgrid applications, and offers a systematic and straightforward design approach using the loop shaping technique. The controller integrates current regulation, management, and limitation that are applicable to microgrids (MGs). The simulation is done by MATLAB/SIMULINK software.

BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

The authors establish a generalized frequency-domain criterion for checking families of polynomials for root confinement in open subsets of the complex plane. The authors show how this criterion reduces to checking certain curves in the complex plane for zero confinement. Moreover, in some special cases, it further reduces to some complex functions with pointwise phase differences that are always less than pi in magnitude. Most of the currently available results on the robust stability of linear systems with parametric uncertainties can be viewed within the unifying frequency-domain framework presented. The framework encapsulates not just finite-dimensional systems, but any linear-time-invariant (LTI) system that can be characterized by transfer functions of a single variable. It also covers robust stability of LTI systems under passive feedback. >

Robust linear controller design of uncertain discrete systems with time-varying delay

Deals with the problem of robust stability of linear systems with uncertain real time-varying parameters with magnitudes and rates of change (or variations, in discrete-time) which are confined to a given convex region. A notion of robust stability, referred to as bi-quadratic stability, which is based on a Lyapunov function that depends quadratically on the uncertain parameters is proposed. LMI based sufficient conditions for bi-quadratic stability of continuous- and discrete-time systems are developed. The proposed stability analysis methods have the advantage that they can be used for solving problems of robust control synthesis, including robust stabilization, robust H/sub 2/ control, and robust H/sub /spl infin// control.

This paper shows how value sets and the zero exclusion principle can be used to obtain results on the robust stability and design of controllers against a special infinite dimensional l/sub 1/ norm bounded parametric uncertainty in both numerator and denominator of scalar discrete-time plants. This parametric uncertainty has properties of both parametric and unstructured uncertainty and allows standard H/sup /spl infin// design tools to be used without conservatism.

Shows how value sets and the zero exclusion principle can be used to obtain results on the robust stability and design of controllers against a special infinite-dimensional l/sub 1/ norm bounded parametric uncertainty in both numerator and denominator of scalar discrete-time plants. This parametric uncertainty has properties of both parametric and unstructured uncertainty and allows standard H/sup /spl infin// design tools to be used without conservatism.

Stabilizability of Bimodal Piecewise Linear Systems With Continuous Vector Field

This paper investigates the stabilization of large scale discrete-time linear control systems by observer-based reduced order controllers. Sufficient conditions are derived for the design of observer-based reduced order controllers for the large scale discrete-time linear control systems by obtaining a reduced order model of the original linear plant using the dominant state of the system. A separation principle has been established in this paper which shows that the observer poles and controller poles can be separated and hence the pole placement problem and observer design problem are independent of each other.KeywordsModel reductionreduced-order controllersstabilizationdominant stateobserversdiscrete-time linear systems

The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system parameter constraints and positive system properties when solving the problem of system quadratic stability. By using an extension of the Lyapunov approach, system quadratic stability is presented to become apparent in pre-existing positivity constraints in the design of feedback control. The approach prefers constraints representation in the form of linear matrix inequalities, reflects the diagonal stabilization principle in order to apply to positive systems the idea of matrix parameter positivity, applies observer-based linear state control to assert closed-loop system quadratic stability and projects design conditions, allowing minimization of an undesirable impact on matching parameter uncertainties. The method is utilised in numerical examples to illustrate the technique when applying the above strategy.

This paper deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals. We propose a new controller parameter optimization approach, which can be carried out experimentally without knowledge of the plant model or the order of the system. The approach has the advantages that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

We propose a parallel algorithm for stabilising large, discrete-time, linear control systems on a Beowulf cluster. Our algorithm first separates the Schur stable part of the linear control system using an inverse free iteration for the matrix disc function and then computes a stabilising feedback matrix for the unstable part. This stage requires the numerical solution of a Stein equation. This linear matrix equation is solved using the sign function method after applying a Cayley transformation to the original equation. The experimental results on a cluster composed of Intel PII processors and a Myrinet interconnection network show the parallelism and scalability of our approach.

Designing minimum variance controllers (MVC) for nonlinear systems is confronted with many difficulties. The methods which are able to identify MIMO nonlinear systems are scarce, and linear models are not accurate in modeling nonlinear systems. In this paper, Vector ARX (VARX) models are proposed for designing MVC and generalized minimum variance controller (GMVC) for linear and nonlinear systems, and the accuracy of these models in approximating the nonlinear MIMO system is studied. However, the VARX is a linear model. It is shown that this model can identify some kinds of nonlinear systems with any desired accuracy. Therefore, the controller designed by the VARX is accurate, even for these nonlinear systems. The proposed controller is tested on a both linear system and a nonlinear four-tank benchmark process. In spite of the simplicity of designing GMVCs for the VARX models, the results show that the proposed method is accurate and implementable.

Networked H∞ control of linear systems with state quantization