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Voltage ripple in single-phase ac–dc converters is usually disregarded to design the dc-link voltage control system, since large dc-link electrolytic capacitors are typically employed. However, replacement of electrolytic capacitors by film capacitors has been widely considered for increasing reliability. Consequently, due to cost constraints, such replacement usually employ low capacitance and may be combined with fast dc-bus voltage controllers. This paper shows that the conventional linear time-invariant (LTI) model may not represent the real converter behavior for reduced capacitance and/or faster controllers, leading to poor system performance or even instability. In this way, for any of these cases, the linear time-periodic (LTP) model is highly encouraged for stability and transient analysis as a tool for the controller design. Experimental results confirm that stability margins are precisely obtained from the LTP model but may not from the LTI model. Finally, this paper also compares both LTI and LTP models while considering the control gain and the dc-bus capacitance size. It is graphically revealed that the phase margin of the LTI model diverges from the LTP model for low dc-bus capacitances and high control gains. [ABSTRACT FROM PUBLISHER]

In this study, the authors propose a control structure for a class of linear time-invariant (LTI) systems with Lipschitz non-linearity and unknown time-varying input delay. This scheme considers the worst-case scenario in control design with truncated prediction feedback approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the non-linear function nor the exact delay function. The truncated prediction deviation is minimised by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of Lyapunov--Krasovskii functionals, sufficient delay--range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design. [ABSTRACT FROM AUTHOR]

This article deals with continuous-time Linear Time-Invariant (LTI) Single-Input Single-Output (SISO) systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed. [ABSTRACT FROM AUTHOR]

We present a formula that computes the output of an R-controllable, regular, single-input linear time-invariant implicit system in such a way that it has prescribed relative degree and zeros. The formula is inspired on different generalizations of Ackermann’s formula. A possible application is in the context of sliding-mode control of implicit systems where, as the first step, one can use the proposed formula to design a sliding surface with desired dynamic characteristics and, as the second step, apply a higher-order sliding-mode controller to enforce a sliding motion along the resulting sliding surface. [ABSTRACT FROM AUTHOR]

The stability of linear time invariant (LTI) systems with independent multiple time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. It is known that for such systems, all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays (Sipahi and Olgac, 2006a). They are called kernel hypersurfaces (KH). The complete description of KH is the only prerequisite for the CTCR stability assessment procedure. As the number of delays increases, however, their evaluation becomes infeasible. Instead, we present a procedure to extract the 2-D cross-sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays. In the 2-delay domain of interest, the exact upper and lower bounds of the imaginary spectra are determined. For this, a combination of half-angle tangent representation of the characteristic equation and the Dixon resultant theory is used as the main contributions of this paper. The complete KH are obtained by sweeping the root crossing frequency in this interval. Using this knowledge CTCR creates the cross-section of the stability map in the domain of the two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones. [ABSTRACT FROM AUTHOR]

In this paper we represent a decentralised LTI control system with decentralised fixed modes (DFMs) by a weighted directed graph and derive sufficient conditions for it to be stabilisable. The sufficient conditions relate to whether the DFMs are decentralised quotient fixed modes (QFMs); decentralised QFMs cannot be shifted by any type of decentralised controller. We use a graph theoretic approach, using existing concepts, and introducing some new ones, to identify the decentralised QFMs for the class of LTI systems that have distinct, repeated, cyclic, or non-cyclic DFMs. It is shown in this paper that a DFM is a QFM, and thus cannot be moved, when some identifiable graphical properties exist. The main results are presented in terms of a Theorem with a constructive proof. Numerical examples are given to illustrate all aspects of the paper. [ABSTRACT FROM AUTHOR]

Swarm stability is studied for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and marginal swarm stability are presented, which require a joint matching between the interactive dynamics of nearest neighbouring vertices and the Laplacian spectrum of the overall network topology. Three numerical instances are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Given a stable linear time-invariant system with tunable parameters, we present a method to tune these parameters in such a way that undesirable responses of the system to past excitations, known as system ringing, are avoided or reduced. This problem is addressed by minimizing the Hankel norm of the system, which quantifies the influence of past inputs on future outputs. We indicate by way of examples that minimizing the Hankel norm has a wide scope for possible applications. We show that the Hankel norm minimization program may be cast as an eigenvalue optimization problem, which we solve by a nonsmooth bundle algorithm with a local convergence certificate. Numerical experiments are used to demonstrate the efficiency of our approach. [ABSTRACT FROM AUTHOR]

Given a feedback control system with an unknown plant, the problem of choosing a stabilizing controller is considered. Working within the framework of unfalsified adaptive control, we consider a finite-dimensional linear time invariant system as a special case of the standard adaptive configuration. A fading memory cost function is presented in which the influence of older data is reduced exponentially. With this cost function, the location of the poles can be detected with only input-output data. Compared with existing results, the cost function can detect changes affecting stability sooner and be used in adaptive switching control to improve the performance of controller switching. [ABSTRACT FROM AUTHOR]

In this study, the problem of input-output finite-time stabilisation of linear time-varying systems is dealt with. The classical definition of input-output finite-time stability (IO-FTS) is extended to that one of structured IO-FTS, which allows to incorporate, in the definition of the stabilisation problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilisation are provided in the case of L∞ and L2 inputs, respectively. Such conditions require the existence of a solution to a certain differential linear matrix inequality. The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model. [ABSTRACT FROM AUTHOR]

In system theory and control, the stability of a given system is an important specification; often we design controllers with stability as the highest priority. A computationally faster algorithm for the Routh–Hurwitz criterion has been discussed in our previous work. This article focuses on computationally fast algorithms and simpler proofs of stability criteria for finite-dimensional linear time invariant (FDLTI) systems. Lyapunov introduced his famous stability theory for both linear and nonlinear systems. In this article, instead of solving the Lyapunov equation and checking its solution for sign-definiteness, we present a new way of testing stability. We rewrite the characteristic polynomial in state-space form, controller canonical form in particular, and check the negative-definiteness of the resulting non-symmetric system matrix A. We demonstrate that this approach provides a bridge between the classical approaches and more modern Lyapunov theory as far as FDLTI systems are concerned. [ABSTRACT FROM AUTHOR]

In this paper, a Kalman canonical decomposition of finite-dimensional linear timevarying continuous-time systems is revisited. Two types of Kalman canonical decompositions are considered; one is collectively dubbed the intervalwise Kalman canonical decomposition and the other is collectively dubbed the global Kalman canonical decomposition. Each type is classified into subtypes resulting from variants of controllabilities (i.e., controllability, reachability, and influenceability) and observabilities (i.e., observability, determinability, and visibility). This paper first investigates the invariance properties of subspaces resulting from variants of controllabilities and observabilities. This paper then gives a self-contained exposition of each Kalman canonical decomposition on an interval. The main result is to prove the existence of intervals on each of which each Kalman canonical decomposition exists. Moreover, the relations among different Kalman canonical decompositions are extensively studied and the inconsistency between the works by Youla and Weiss is resolved. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a simple method for identifying first- and second-order processes with dead-time by using moments of a single rectangular pulse response in an open-loop system. A closed-form formula is proposed to determine all parameters of four types of process models for a stable linear time-invariant process. It is shown that the same approach can be extended to the identification of multi-input, multi-output linear processes. It is demonstrated through a comparative analysis that the proposed identification method results in good accuracy with a noisy output, and is also able to closely approximate various high-order processes in those low-order models. [Copyright &y& Elsevier]

Abstract: This paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples. [Copyright &y& Elsevier]

Abstract: This paper studies control problems for discrete-time single-input linear time-invariant plants when controlled over a signal-to-noise ratio (SNR) constrained channel. Our focus is on the performance limitations in an architecture that uses channel feedback. We explicitly characterize the interplay between stabilization, optimal performance, and SNR constraints, highlighting the way in which plant dynamical features affect the best achievable performance. We also apply our results to the study of networked control systems where communication takes place over a power constrained erasure channel. In that scenario, we first show that stabilization problems, and problems involving stationary second-order moments, can be dealt with by focusing on a related SNR constrained networked situation. This observation allows one to obtain results valid in the alternative scenario as corollaries of the results obtained when a single SNR constraint is present. [Copyright &y& Elsevier]

This study investigates the exponential stability analysis problem for continuous-time and discrete-time positive linear systems with delays. For given decay rate, necessary conditions for exponential stability of such systems are presented based on the asymptotical stability results of positive linear time-delay systems, and sufficient conditions are provided by using Lyapunov-Krasovskii functional method. It is shown that, the exponential stability with given decay rate of positive linear time-delay systems has to do with the delays. Some illustrative examples are given to show the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]