Dilated LMIs Research Articles

Robust H∞ control of an uncertain bilateral teleoperation system using dilated LMIs

A robust state-feedback [Formula: see text] controller is proposed for an uncertain bilateral teleoperation system having norm-bounded parametric uncertainties on mass and damping coefficients of the considered master/slave system. The proposed method ensures robust stability and successful reference tracking and force reflection performance. While Lyapunov stability is used to ensures asymptotic stability, the [Formula: see text] norm from exogenous input to the controlled output is utilized in satisfying the reference tracking and force reflection. As two performance objectives and robust stability requirement are conflicting with each other, the proposed controller reduces the associated conservatism with dilated linear matrix inequalities. Standard and dilated linear matrix inequality-based robust [Formula: see text] state-feedback controllers are performed with a one degree of freedom uncertain master/slave system under reference signal and environmental-induced exogenous force. Numerical simulation results show that the dilated linear matrix inequality-based [Formula: see text] control satisfies lower [Formula: see text] norm than a standard [Formula: see text] control. Moreover, the proposed controller demonstrates a very successful performance in achieving performance objectives despite the stringent norm-bounded parameter uncertainties.

Computation of low-complexity control-invariant sets for systems with uncertain parameter dependence

This paper considers the problem of computing a low-complexity robust control-invariant (LC-RCI) set for uncertain systems, along with a static linear state-feedback law. The LC-RCI set, assumed to be symmetric around the origin and described by the same number of affine inequalities as twice the dimension of the state vector, is the result of an iterative procedure, where semi-definite programs (SDPs) are solved at each step. The SDPs are formulated to increase the LC-RCI volume at each step, subject to tractable reformulations of the system constraints as well as the invariance condition (in the form of standard or dilated LMIs), and a new approach to determinant maximization. The two proposed algorithms are applicable to systems with rational parameter dependence, which cannot be handled with the existing similar approaches without introducing additional conservatism.

A further remark on the problem of reliable stabilization using rectangular dilated LMIs

In this brief paper, an extension of the result of Fujisaki & Befekadu (2009, Reliable decentralized stabilization of multi-channel systems: a design method via dilated Linear Matrix Inequalities (LIMs) and unknown disturbance observers. Int. J. Contr., 82, 2040–2050.) concerning the problem of reliable stabilization for generalized multi-channel systems is given. Specifically, we use a rectangular dilated LMIs framework to provide a relaxed sufficient condition for the reliable stabilization of a multi-channel system both when all of the controllers work together and when one of the controllers ceases to function due to a failure.

On Reliable Stabilization via Rectangular Dilated LMIs and Dissipativity-Based Certifications

In this short note, we consider the problem of reliable stabilization for multi-channel systems, where our main objective is to maintain the robust stability of the perturbed closed-loop system when there is a single controller failure in any of the control channels. Specifically, we present a less-conservative result than results in the literature in terms of a set of dilated LMIs for the reliable state-feedback stabilization of the nominal system, while a dissipativity-based certification is used to extend the stability condition when there is an additive model perturbation in the system. Finally, a numerical example is presented to illustrate the applicability of the proposed technique.

Parameter Reduction for Disturbance Attenuation with a Discrete-Time LPV Controller

This paper considers the application of a discrete-time LPV controller technique to active noise and vibration control (ANC/AVC) based on dilated LMIs. The goal of the controller design is to reduce the excitations induced by the combustion engine and transmitted through the chassis into the passenger compartment. These vibration disturbances are quite specific and consist of a varying nominal frequency and several multiples of it. The main contribution of this paper focuses in the modeling of the multisine disturbance. A parametrization of the cosine-function is proposed requiring only two parameters for L different frequencies. This reduction is based on a least square approximation. By separating the Lyapunov matrix and the system matrix in the controller design it is possible to use a Lyapunov function with dependent Lyapunov matrices leading to less conservative results. Simulations show the benefit of this method by attenuating six predefined frequencies with only two varying parameters.

Reliable decentralised stabilisation of multi-channel systems: a design method via dilated LMIs and unknown disturbance observers

Reliable decentralised stabilisation is considered for general multi-channel plants, where the objective is to maintain stability of the closed-loop system when all of decentralised controllers work together and when one of the controllers is extracted due to a failure. For this control problem, a design method is presented, where a dilated LMI technique is employed for deriving reliable state feedback design, while a version of unknown disturbance observer is used as a decentralised observer for extending the design to output feedback case. Applicability of the proposed method is demonstrated through a power system example, where a model reduction and a low pass filter are further employed.

New Dilated LMIs to Synthesize Controllers for a Class of Spatially Interconnected Systems

This paper presents sufficient conditions based on dilated LMIs to analyze and synthesize controllers that minimize the L 2 -norm of the the closed-loop system for spatially varying interconnected polytopic systems. The approach presented here searches for a parameter dependent Lyapunov function (PDLF) by dilating the original LMIs. This dilation not only helps in the search for a PDLF but also introduces extra degrees of freedom which may result in further reduction of conservatism. Approaches to synthesize full-order polytopic controllers and reduced-order, reduced-structure controllers are also presented here.