Input-output stability of linear time-invariant systems

In this paper is studied the stabilization problem by state-derivative feedback for linear time-invariant continuous-time systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system, obtained by state-derivative feedback from the given linear time-invariant continuous-time system. Furthermore a procedure is given for the computation of stabilizing state-derivative feedback. Our approach is based on properties of real and polynomial matrices.

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.

: 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.

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. >

The problem of sampling-time robustness of a hybrid system arises in various practical applications such as computer-aided manufacturing (CAM), robotics, minicomputer systems design and other areas where miniaturization is of primary importance. The paper investigates inherent stability properties of hybrid closed-loop multivariable systems. In particular, the system robustness is studied with respect to the sampling time interval. A practical criterion is obtained to determine the critical sampling time value for linear time-invariant systems using the frequency domain technique. The general result is applied to a closed-loop control system. For the case of a single-input single-output three-dimensional hybrid control system, the critical sampling time is calculated using the derived frequency domain stability criterion. A practical implementation diagram is also provided. Optimal hybrid approximations are considered for both open-loop and closed-loop control systems. Their comparative stochastic perform...

This work addresses the output feedback stabilisation problem for a class of linear single-input single-output systems subject to I/O network delays. More precisely, we are interested in the characterisation of the set of delay and gain parameters guaranteeing the stability of the closed-loop system. To perform such an analysis, we adopt an eigenvalue perturbation based approach. Various illustrative numerical examples complete the presentation.

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.

Nature has the key to solve every single problem that exists. This paper strives to propose a method which is based on flower pollination algorithm to acquire a stable reduced order model (ROM) of a higher order linear time-invariant (LTI) system. The suggested method utilizes Pade-based moment matching technique to deduce denominator approximants for the reduced order system, whereas the reduced order approximants of numerator polynomial are obtained using flower pollination (FP) algorithm. To prove the viability of the suggested method, numerical examples are solved considering single-input single-output (SISO) systems. A comparison has been drawn between suggested method and existing methods which are available in the current literature and is presented in this paper. This comparison is founded on a performance index which is known as integral square error (ISE).

The paper deals with the identification of linear time invariant (LTI) systems by a special observer. An observer emitting an frequency modulated continuous wave (FMCW) signal and having a stretch processor as receiver will be considered for system identification. A thorough derivation of the gathered baseband signal for arbitrary LTI systems will be given. It is shown, that the received signal is approximately given by the transfer function of the LTI system over the frequency sweep of the FMCW signal. The proof relies on an infinite large time-bandwidth product of the transmit signal, such that errors remain in practical applications with a finite time-bandwidth product. Monte–Carlo simulations are conducted to verify the approximation and to quantify its accuracy and remaining errors. The findings are important for e.g. calibration or derivation of a device model in FMCW radar applications.

Chapter 4 - Frequency Analysis: The Fourier Series

This study investigates characteristic root equivalency relations between commensurate order and integer order Linear Time Invariant (LTI) systems. Author introduces some useful properties of a special class of commensurate order systems, which is called characteristic root equivalency class of LTI systems. These properties present potential to facilitate design and analysis efforts of this class of commensurate order systems. In this sense, straightforward stability checking procedures and design approaches for commensurate order root equivalent systems of the first and second order LTI systems are demonstrated. Findings of the study are validated by illustrative examples.

This paper presents a sufficient condition that establishes closed loop stability for linear time invariant dynamical systems with transfer functions that are analytic in the open right half complex plane. The condition is suitable for analyzing a large class of highly complex, possibly interconnected, systems. The result is based on bounding Nyquist curves by using frequency dependent half planes. It provides (usually non-trivial) robustness guarantees for the provably stable systems and generalizes to the multidimensional case using matrix field of values. Concrete examples illustrate the applications of the condition. From our condition, it is easy to derive a relaxed version of the classical result that the interconnection of a positive real and strictly positive real linear system under feedback is closed loop stable.

We discuss the stabilization of large scale linear time invariant dynamical systems via feedback. An overview of efficient schemes based on the discrete Riccati difference equation are presented. In particular, results are given for a Newton-like approach to the problem.

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.

A matrix-operator representation of parameter sensitivities is used to provide an algebraic "structural" analysis of local parameter identifiability in linear time-invariant ordinary differential equation systems. Necessary conditions for identifiability depend only upon the system matrices, no integrals must be computed, and arbitrary parametrization may be used. Relations to insensitivity are discussed, and design techniques are suggested which use the nonidentifiable (insensitive) subspace to systematically reduce the number of exciting parameters in individually designed parameter identification experiments. Finally, sufficiency conditions for zero-state identifiability are examined in terms of control inputs which continually excite the natural modes of the parameter sensitivities.