Controller Design for Multivariable Linear Time-Invariant Unknown Systems

Eigenvalue-optimization-based stabilization of multi-input multi-output linear time-invariant systems is considered. The system is allowed to be a retarded time-delay system with discrete time-delays. No restriction has been made on the number of time-delays. Instead of conventional static or dynamic delay-free output feedback, delayed output feedback is considered in the controller part. Furthermore, in the case of multi-input and/or multi-output, the controller is allowed to introduce a different time-delay in each input-output channel. Benchmark examples illustrate the effectiveness of the proposed method.

Blending based multiple-model adaptive control of multivariable systems with application to lateral vehicle motion control

This paper researches fault-tolerant control for discrete-time multi-input multi-output (MIMO) linear time-invariant (LTI) systems with both matched and unmatched uncertainties. A discrete-time integral sliding mode (DISM) controller and an improved direct method for control allocation are proposed as the reconfigurable control method. Closed-loop stability with matched and unmatched uncertainties for discrete-time MIMO LTI systems with DISM is studied, and the accuracy boundaries for are determined for the final states. A spacecraft model is simulated with multi-faults, efficiency factor inaccuracies, matched uncertainties, and unmatched uncertainties, which exemplifies our FTC scheme.

Consistent estimation of real NMP zeros in stable LTI systems of arbitrary complexity

On Reconfigurability

Given a stable linear time-invariant dynamical system x·= Ax, it is shown that there exists a related stable family of dynamical systems x·=A(k)x. The Lyapunov stability criterion remains valid for all linear operators A(k)=DkA of this family.

In this paper, new sufficient-condition bounds on linear time-varing perturbations that maintain the stability of an asymptotically stable linear time-invariant nominal system are obtained for structured (elemental) independent perturbations. A sufficient condition for the stability of interconnected dynamic systems is also presented in terms of a bound on the time-varying structural parameter. Some examples are given to compare these proposed bounds with those existing bounds.

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

In this paper we analyze proportional-derivative output feedback control for single-input single-output linear time-invariant dynamical systems with discrete state delays. The main focus of the presented work is the analysis of the effect of arbitrarily small implementation errors, such as a feedback delay or a finite-difference approximation of the derivative, on the stability of the closed loop. More specifically, it will be shown that the classical notion of stability does not suffice to adequately describe the asymptotic behavior of the closed loop system in the presence of these implementation errors, as stability might be lost even when these errors are made arbitrarily small. This paper therefore considers strong stability, which eliminates this well-posedness problem by not only requiring stability but by also enforcing that stability is preserved for sufficiently small perturbations. To conclude this paper, a controller design methodology for proportional-derivative output feedback controllers that strongly stabilize the system, is proposed.

In this paper, the stability and control of linear systems with parameter uncertainty are considered. The characteristic equations of such systems are derived as functions of uncertain parameters. The cases in which the coefficients are polynomial functions of the uncertain parameters are studied and an algorithm is presented for the calculation of stability margins in the parameter space in general lp-norms. The stability is defined with respect to arbitrary regions in the complex plane (so-called D-stability). The algorithm requires a search on the contour of the region (frequency search) and to solve a system of equations at each step. Using the above algorithm, a method is also presented for the design of robust controllers for systems with uncertain parameters and robust pole placement inside the regions of interest is addressed.

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.

We consider the problem of blind source separation of independent signals which passed through a multi-input multi-output linear time-invariant system. An approximate maximum likelihood estimator and its performance were studied by Yellin and Friedlander (see IEEE Trans. Signal Processing, vol.47, no.5, p.1410-14, 1999, and vol.47, no.6, p.1542-58). The results derived therein are used here to study the performance of source separation techniques based on high order statistics.

ROBUST STABILITY ANALYSIS FOR STRUCTURED UNCERTAINTIES WITH BOUNDED VARIATION RATES

Comments on ‘practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models’

This paper deals with the question of the existence of weak and strong common
\nquadratic Lyapunov functions (CQLFs) for stable discrete-time linear timeinvariant
\n(LTI) systems. The main result of the paper provides a simple characterisation
\nof pairs of such systems for which a weak CQLF of a given form exists
\nbut for which no strong CQLF exists. An application of this result to second
\norder discrete-time LTI systems is presented.