Stabilization of Linear Time-Invariant Systems by State-Derivative Feedback

We study the decentralized stabilization problem of linear time-invariant large scale interconnected systems with delays. We obtain a sufficient decentralization condition for unforced systems and use this analysis result to obtain a decentralized state-feedback controller using standard H/sub /spl infin// control theory. We also obtain a decentralized observer for the interconnected system.

The Nyquist stability criterion and the notion of type n systems have been extended from lumped parameter systems to a larger class of linear single-loop single-input single-output time-invariant systems, with constraints presented in the text.

This paper is concerned with the nonlinear static state feedback stabilization of time-invariant linear multivariable continuous-time systems with friction driven backlash in the control inputs. A time-invariant static nonlinear state feedback compensator is proposed, easily obtainable solving an algebraic Riccati equation. The global asymptotic stability of the resulting closed-loop nonlinear system is proved using the Lyapunov's direct method and the La Salle's invariance principle. A simulation study shows that the proposed nonlinear state feedback compensator achieves an overall stabilization performance significantly better than the known backlash inverse compensator.

Based on complex scaling, the paper copes with stability analysis and stabilization of linear time-invariant continuous-time systems with multiple time delays in state, control input, and measured output, under state and/or output feedback. More specifically, the paper establishes stability criteria for exponential/asymptotical stability with Hurwitz complex scaling being applied to the related characteristic polynomials. The stability conditions are necessary and sufficient, delay-dependent, and independent of feedback structures and open-loop poles distribution. The criteria can be implemented graphically with locus plotting or numerically without it; moreover, no prior frequency sweeping is involved, and the contour and locus encirclement orientations can be self-defined. Exploiting the complex scaling approach and embracing its technical merits, it is considered to design static state feedback control for robustly stabilizing time-delayed systems. A small-gain interpretation for the suggested stabilization is also elaborated. Examples are included to illustrate the main results.

: 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.

Vision-based robotic applications with aggressive maneuvers suffer from the low sensing speed of standard cameras that sample frames at constant time intervals. On the other hand, although neuromorphic vision sensors are promising candidates to provide the needed high-frequency sensing, a new class of algorithms needs to be synthesized that can deal with the uncommon output from each pixel of these sensors, which (independently of other pixels) fire an asynchronous stream of “retinal events” once a change in the light field is detected. In this paper, we investigate the problem of stabilizing a stochastic continuous-time linear time invariant system using noisy measurements from a neuromorphic vision sensor. We propose an H ∞ controller that addresses this problem and provide the critical event-generation threshold for these neuromorphic vision sensors and characterize the statistical properties of the resulting states. The efficacy of our approach is illustrated on an unstable system.

This paper considers the problem of robust stabilization of non-minimum phase linear time-invariant single-input single-output uncertain systems. Under certain assumptions, it is shown that non-minimum phase LTI uncertain systems with known order and known and invariant relative degree can be controlled to achieve robust stability by using a linear periodic output feedback controller. The authors' result generalizes similar results for LTI minimum phase uncertain systems. >

In this paper, the cooperative stabilization problem of linear time-invariant (LTI) systems is studied based on a class of distributed Luenberger observers. A given LTI system is estimated by a network of observers. In case of observability configuration or external attack, each observer has to possess different measurement output of the LTI system. Classical distributed control strategies cannot be directly used because they are assumed to obtain identical information. In view of this problem, a class of distributed observers are designed under an undirected graph, which can recover the state of the LTI system by limited local information. By using any single channel of the estimated state, a control input is proposed to stabilize the LTI system. By analysing the stability of an augmented system which involves the LTI system and the estimation error system, some necessary and sufficient conditions are derived for the existence of control gains that guarantee the stabilization of the LTI system. In addition, some algorithms are proposed to specify the control gains. Lastly, some simulation examples are given to verify the effectiveness of the theoretical result.

This paper considers the problem of constrained stabilization of linear continuous-time systems when a quadratic cost criterion is imposed in the design of the state feedback control law. The linear quadratic regulator (LQR) is solved under positivity constraint, which means that the resulting closed-loop systems are not only optimally stable, but also positive. We focus on the class of linear continuous-time positive systems (Metzlerian systems) and use the interesting properties of Metzler matrices to provide the necessary ingredients for the main results of the paper. A two-step procedure is proposed to solve the problem. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the Metzlerian constraint, and the constrained stabilization is solved using linear programming (LP) or linear matrix inequality (LMI). Second, a sufficient condition is outlined for the existence of a solution to maintain the positivity of the first step while achieving the optimality of LQR. Finally, the robustness of the design is analyzed and possible extension of the design is proposed for an uncertain interval systems. A numerical example is included to illustrate the procedure.

This note is concerned with stabilization of continuous-time periodic linear (CPL) systems with state feedback. The design is based on solutions to a class of parametric periodic Lyapunov differential equations (PLDEs) resulting from the problem of minimal energy control with guaranteed convergence rate. By carefully studying the properties of the PLDEs and their solutions, a continuous periodic state feedback is designed. The PLDE based approach is effective in designing stabilizing controller for CPL systems as the designers need only to solve a linear differential equation whose solution can be obtained analytically if the system is relative simple and can be computed numerically by integration in general cases. Necessary and sufficient conditions on the free parameter in the PLDE are proposed to guarantee the stability of the closed-loop system whose characteristic multiplier set can even be exactly computed accordingly. A numerical example is worked out to show the effectiveness of the proposed approach.

We consider linear time-invariant continuous-time systems x/spl dot/(t)=Ax(t)+bu(t), y(t)=cx(t) with 2-dimensional state x/spl isin//spl Rscr//sup 2/, scalar input u/spl isin//spl Rscr/, and scalar output y/spl isin//spl Rscr/. The matrices A,b and c are constant and of appropriate dimension. We discuss the problem of making the above linear system exponentially stable by means of a static time-varying output feedback u(t)=k(t)y(t). Easily verifiable necessary and sufficient conditions for this problem to be solvable are presented. Moreover, the proof of the sufficiency part is constructive; that is, it supplies the required feedback gain k(t). The paper thus solves an open problem posed by R. Brockett (1998) for the particular case of scalar input scalar output second-order systems. We assume throughout the paper that b/spl ne/(0 0)/sup T/ and c/spl ne/(0 0).

Frequency-domain stability conditions for asynchronously sampled decentralized LTI systems

A new method for computing delay margins for stability of linear delay systems

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.

This paper is concerned with the problem of designing linear time-invariant control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues in the interval shown in figure 1. This new algorithm can also be used for the placement of closed-loop eigenvalues in a specified interval in z-plane and can be employed for large-scale linear time-invariant control systems. Some illustrative examples are presented to show the advantages of this new technique.