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The main objective of loop shaping design methodology is to produce a controller that guarantees robust stability against normalized coprime factor uncertainty. This form of uncertainty was used by Glover and McFarlane [6–8] to obtain an exact solution to the robust stabilization problem. The order of loop shaping controller is typically as high as the model order. Such high order controllers are...
A nonlinear missile model with time-varying uncertain parameters is controlled with a simple feedback linearisation and time-scale separation design, with synthesis based on the nominal model and full state feedback. The closed-loop system is then represented as a linear fractional transformation (LFT). A robust H∞ filter is designed for the controlled plant, to estimate unknown states. Robust stability...
This paper revisits the issue of robust stability analysis of linear interval parameter matrices, which used to be a highly active research topic in the eighties and nineties. The reason for this revived interest in this topic is that the recent research by the authors on Qualitative Stability, a topic of interest in the field of population/community dynamics in ecology is shown to shed considerable...
Different variants of the S-procedure provides a very important tool in robust stability and robust performance analysis. Concerning performance assessment this paper shows that the design framework based on the full block S-procedure (extended KYP lemma) contains an inherent conservativeness. The main result of the paper is a multivariate version of the classical S-procedure, stated for negative...
In this paper for the class of continuous time nonlinear uncertain singular time delay dynamical systems we present robust stability analyze results. Next, we consider a control problem for nonlinear continuous time uncertain singular time delay dynamical systems involving a notion of optimality with respect to an auxiliary cost which guarantees a bound on the worst-case value of a nonlinear-nonquadratic...
This paper applies results on the robust stability of nonlinear quantum systems to a system consisting an optical cavity containing a saturated Kerr medium. The system is characterized by a Hamiltonian operator which contains a non-quadratic term involving a quartic function of the annihilation and creation operators. A saturated version of the Kerr non-linearity leads to a sector bounded nonlinearity...
In this study, an initial robust stability analysis procedure is proposed to test the performance of the designed U-pole placement control systems. Unlike the classical design procedures for non-linear control systems, the control-oriented U-model based non-linear control systems cancel the non-linearity of the non-linear models. Therefore, the closed loop transfer function of U-pole placement control...
Recent robust stability analysis results for linear time-varying feedback interconnections are based on a time-varying generalisation of the ν-gap metric. The causality of closed-loop mappings is dealt with explicitly, rather than via well-posedness assumptions as is common in the literature. Here, an alternative time-varying gap metric is defined. It is shown that this gives rise to corresponding...
In this paper, a fixed order H∞ synthesis is used to directly shape the open loop transfer function so that it matches as closely as possible, in the singular values sense, a desired frequency gain which captures both performance and robust stability objectives. First, a loop shaping weight is automatically computed, and then it is used in the controller synthesis by solving a well-suited four-block...
In this paper we continue our efforts to arrive at a solution of the gain-scheduling controller design problem with dynamic multipliers. Although a solution for D-scalings is available, this scenario leads to conservatism if scheduling on real parameters. This motivates to consider the very same problem with D/G-scalings, for which we recently proposed a design framework with generalized positive...
This paper deals with a robust stabilization problem of discrete model-reference control systems on integer grid coordinates. At present, all feedback control systems are realized using discretized signals. However, the analysis and design of discrete-time and discrete-value (point-to-point) control systems has not been established. In this paper, the robust stability of that type of discretized control...
A pitch rate controller is designed for a linear parameter-varying (LPV) model of the short-period longitudinal dynamics of ADMIRE, using input-output linearisation. A scaled linear differential inclusion (LDI) technique is applied to verify stability of the parameter-varying zero-dynamics. The parameters (Mach and altitude) are allowed to be time-varying. The proposed controller is simulated in the...
In this paper a class of Piecewise Quadratic Lyapunov Functions (PQLFs) for the analysis of the robust stability of linear systems subject to polytopic uncertainties is considered. These functions are obtained by partitioning the state space into polyhedric conical sets and by associating to each cone a quadratic form. This class of Lyapunov functions is not only a generalization of quadratic Lyapunov...
This article considers the robust stabilization problem of uncertain linear-time invariant plants with coprime factor uncertainty bounded in ℛℋ∞. The problem considered here is a generalization of the normalized coprime factor robust stabilization problem. It is shown that the problem admits a simple and intuitive controller implementation parameterized in terms of a state-feedback matrix F and observer...
In this paper we generalize our previous results on robust controller synthesis to robust gain-scheduled controller synthesis. We present novel insights that reveal how the robust gain-scheduled controller synthesis problem can be turned into a semi-definite program, under the hypothesis that (i) the control channel is not affected by uncertainties and (ii) the uncertainties and scheduling variables...
This paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ⊆ ℝn. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties...
This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows...
For discrete-time piecewise affine systems, exponential stability and quadratic performance are analyzed in the presence of disturbances. Our approach is based on constructing a sequence of finite-state symbolic models for the piecewise affine system and analyzing the robust stability and performance of any of these symbolic models using linear matrix inequalities. The presented analysis is scalable;...
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system coupling operator. Then, the special case of a nominal linear quantum system is considered with non-linear perturbations to the system coupling operator. In this...
This paper applies recent results on the robust stability of nonlinear quantum systems to the case of a Josephson junction in a resonant cavity. The Josephson junction is characterized by a Hamiltonian operator which contains a non-quadratic term involving a cosine function. This leads to a sector bounded nonlinearity which enables the previously developed theory to be applied to this system in order...
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