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In this paper, two alternative control procedures are compared for a spatially three-dimensional distributed heating system. In both cases, the system model is derived as a finite volume representation that assumes a piecewise homogeneous distribution of the temperature in each finite volume element. The parameterization of both control strategies is performed by using linear matrix inequalities in...
Problems of optimal pole placement for linear time invariant systems via state feedback have been studied for several decades. The minimum gain pole exact placement problem involves obtaining a feedback matrix that will assign a certain desired set of closed-loop poles, while also minimizing the gain (matrix norm) of the feedback matrix. Numerous methodologies have appeared in the literature to address...
In this contribution the backstepping design of flatness-based tracking controllers for parabolic systems is extended by an integral action to acount for exogenous disturbances and model uncertainty. The proposed controller design only amounts to stabilizing an ODE by eigenvalue assignment and to applying the standard backstepping approach to a parabolic PDE. The robustness of the resulting disturbance...
This paper addresses the fundamental problem of improving the Luenberger Observer (LO)-based feedback control so that it can deal with effectively a wide range of uncertainties, both internal and external. It is shown that the effect of such uncertainties can be estimated and cancelled in real time, all based on the yet untapped source of information: the estimation error in the existing LO. The result...
In this paper, we study the robust output regulation problem for linear systems subject to both input time-delay and communication delay via the internal model design approach. Due to the presence of the communication delay, the classical internal model has to be modified so that its dynamics can depend on the delayed state or error-output measurement. A framework for handling the robust output regulation...
This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent...
This paper provides synthesis conditions of robust state feedback control law for continuous-time linear time-invariant systems with polytopic uncertainty. By conveniently expressing the Lyapunov stability condition of the closed-loop system and using the elimination lemma, a new LMI synthesis condition with scalar searches is proposed. As main novelty, the scalar search is constrained to the interval...
In this paper, we develop a distributed state-feedback controller synthesis algorithm for a discrete-time LPV system that is composed of the interconnection of several sub-systems each scheduled by its own parameters. A set of LMI conditions are derived for robust ℒ2-gain performance of such a system in the framework of multiplier-based LPV synthesis. The results have been oriented to be applied in...
This paper provides a technique for admissibilization of linear descriptor systems by state derivative feedback. Sufficient conditions are derived for the closed-loop system to be admissible are given in terms of linear matrix inequalities (LMIs). So, these conditions are reliable using numerical computations. An explicit expression of the desired derivative state feedback control law is also given...
A design method of decentralized local robust state feedback controllers is presented for a class of uncertain large scale interconnected time-delay dynamical systems. In this paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any nonnegative constants. A class...
In this contribution parameterizations of constant state feedback controllers are given that assign the closed-loop eigenvalues of a linear system to predefined locations and encompass, besides the degrees of freedom due to the controller, freedom in the choice of system parameters. These parameterizations are subsequently used in an optimization procedure in order to simultaneously obtain a controller...
In this paper, decentralized guaranteed cost control for uncertain large-scale singular systems are studied. The parametric uncertainty which is assumed be norm-bounded exists not only in system matrices, but also in a derivative matrix. For the stabilization of the given system, guaranteed cost proportionalplus-derivative state feedback is suggested. The linear matrix inequality (LMI) condition which...
In this paper, the conservativeness issue is addressed for networked control of discrete time systems through a quantized lossy channel. The quantized lossy channel is first characterized as an uncertainty disturbance in signal-to-noise-ratio forms with both the input and output signals of the channel. Then it is shown that appropriate uncertainty characterization should be applied to conduct robust...
This paper investigates the distributed robust control problem of multi-agent systems with general linear dynamics and under directed communication topology. The dynamics of each agent is subjected to independent norm-bounded uncertainties, making the system heterogenous to some extent. By utilizing M-matrix approach, an algorithm is proposed for the parameters' designs to ensure the stabilization...
This paper investigates the problem of robust stabilization of uncertain saturating actuator systems with a time-varying delay in both state and control. Employing the Razumikhin approach for the stability of functional differential equations, upper bounds on the time-varying delay are proposed such that the considered uncertain system is robustly globally or locally asymptotically stabilizable via...
In this paper we consider frequency properties and robustness of H∞ suboptimal state feedback. It is shown that in spite of large gain and phase margins (at the plant input), the closed-loop H∞ suboptimal system may not be robust in the sense that small parameter variations in the plant and/or the controller matrices may lead to instability. This situation is illustrated by a simple example.
A multirate controller for the coupled mass benchmark problem is presented. A robust controller with full state feedback is designed using LMI techniques, and the transfer properties of state feedback control are approximately recovered by using a very simple fast output sampling control law. The proposed controller is compared to a state feedback / loop transfer recovery solution reported in the...
The inverted pendulum is used as an example to illustrate controller fragility under minimum norm state feedback. The stabilization process gets trapped in a cusp. A parameter space representation shows a safe escape.
Explicit piecewise linear state feedback solutions to the constrained linear model predictive control problem have been characterized and computed using multi-parametric quadratic programming. The piecewise linear state feedback is defined on a polyhedral partition of the state space, which may be quite complex. Recently, approximate multi-parametric quadratic programming approaches have been developed,...
This paper is concerned with the mixed H2/H∞ control problem. The purpose of this paper is to give an iterative algorithm for finding a sub-optimal static state feedback controller for the mixed H2/H∞ control problem. The key idea of our algorithm is to construct two “controller sets”: one is a set of controllers that improve the H2 norm of the closed loop map for a given controller and the other...
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