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A linear time-invariant (LTI) system's controllability radius measures the norm of the smallest parametric perturbation such that the perturbed system is uncontrollable, and is of practical importance. In this note, we study the real controllability radii of i) higher-order systems; ii) descriptor systems; and iii) time-delay systems, where the perturbations are restricted to the set of real values, and the spectral norm is considered. Formulas for these radii are presented using a framework involving generalized real perturbation values, which has certain computational advantages over other formulations found in the literature. In particular, the formulas are readily more computable, especially for higher-dimensional systems, and a minimum-norm perturbation can also easily be obtained. Numerical examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider the use of a linear periodic controller (LPC) for the control of linear time-invariant (LTI) plants in the decentralized setting. If a plant has an unstable decentralized fixed mode (DFM), it is well known that no decentralized LTI controller can stabilize it, let alone provide good performance. Here we show that, if the plant is centrally controllable and observable and the graph associated with the plant is strongly connected, then even if the plant has an unstable DFM, we can still design a decentralized LPC to provide LQR performance as close to the centralized optimal performance as desired; the proposed controller in each channel consists of a sampler, a zero-order-hold, and a discrete-time linear periodic compensator, which makes it easy to implement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The decentralized robust servomechanism problem (DRSP) for colocated large flexible space structures (LFSS) under sensor and actuator failures is considered. A unified treatment of failures is enabled by introducing failure matrices. For colocated LFSS, stabilization, tracking of constant set points, and regulating against constant disturbances such that no “spillover effects” occur, can be simultaneously handled using a fault-accommodating decentralized tuning PID error-feedback controller. Necessary and sufficient conditions for solvability of the DRSP for colocated LFSS under sensor and actuator failures are derived in our analysis. In the case when each control agent is single-input/single-output, the decentralized fault-tolerant controller becomes particularly simple to implement. Steady-state output matrices for failed outputs are computed, and are found to be independent of controller gains. [ABSTRACT FROM AUTHOR]

In this technical note we study the servomechanism problem for positive open-loop stable LTI systems under constant tracking signals and constant disturbances. In particular, we show that in general the MIMO servomechanism problem for positive systems is not solvable, but is solvable for various classes of MIMO systems, and for the class of SISO systems in which the disturbances are small compared to the tracking signal. In particular, we give existence results as to what subclass of reference and disturbance signals can be considered, for the case when either the mathematical model of the plant is known or unknown, and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals. [ABSTRACT FROM PUBLISHER]

In this note, we present a simple and readily computable formula for the calculation of the real controllability/stabilizability and observability/detectability radii for linear time-invariant systems. [ABSTRACT FROM AUTHOR]

In the design of conventional control systems for a multivariable system, using robust/adaptive control techniques, the motivation is to design a controller which "works satisfactorily'' in the presence of plant uncertainty. Unfortunately, however, if large unanticipated structural changes subsequently occur in the system, severe limitations in practical performance may occur, since such conventional control schemes usually do not have the ability to control systems which are subject to unplanned extreme changes. Moreover, for the realistic situation when control input constraints exist, few results for continuous time multivariable systems are available. In this paper, a new class of self-tuning proportional-integral-derivative switching controllers, which is an extension of the self-tuning integral controller of Miller and Davison, is described, and has the property that it is robust to unplanned extreme changes in the plant and satisfies any feasible control signal input constraints. Results of this self-tuning controller when applied to an experimental multivariable system also are described. [ABSTRACT FROM AUTHOR]

Studies the cheap control problem for discrete time linear time-invariant systems. Attempt to obtain fundamental limitations for error tracking/regulation for the servomechanism problem for a sampled system; Cheap control problem for discrete systems; Algorithm to perform the factorization.

Examines the decentralized stabilization and servomechanism problem for descriptor systems. Characterization of algebraic constraints on plant state variables; Decentralization of impulsive fixed mode systems; Determinants of the solvability of the decentralized robust servomechanism for descriptor systems.