Search results for "linear matrix"

A passivity approach to control of Markovian jump systems with mixed time-varying delays

2013

This paper investigated the problem of control design for a class of stochastic systems with Markovian jump parameters and time-varying delays. For the model under consideration, a passivity-based approach is introduced for designing mode-dependent output feedback controllers with mixed discrete and distributed delays. A Lypunov-Krasovskii function (LKF) is defined to establish new required sufficient conditions for ensuring exponentially mean-square stability and the passivity criteria, simultaneously. Moreover, controller gains are calculated based on a convex optimization method by solving a Linear Matrix Inequality (LMI). Finally, simulation results are provided to illustrate the effect…

Delay-Range-Dependent Linear Matrix Inequality Approach to Quantized H∞ Control of Linear Systems with Network-Induced Delays and Norm-Bounded Uncert…

2010

This paper deals with a convex optimization approach to the problem of robust network-based H∞ control for linear systems connected over a common digital communication network with static quantizers. Both the polytopic and the norm-bounded uncertainties are taken into consideration separately. First, the effect of both the output quantization levels and the network conditions under static quantizers is investigated. Second, by introducing a descriptor technique, using a Lyapunov—Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities for the existence of the desired network-bas…

Robust control of uncertain multi-inventory systems via linear matrix inequality

2008

We consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of "-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which "-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.

model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information

2013

This paper investigates the problem of model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear…

Notice of Violation of IEEE Publication Principles: Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

2013

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

2008

Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The result…

Efficient Pruning LMI Conditions for Branch-and-Prune Rank and Chirality-Constrained Estimation of the Dual Absolute Quadric

2014

International audience; We present a new globally optimal algorithm for self- calibrating a moving camera with constant parameters. Our method aims at estimating the Dual Absolute Quadric (DAQ) under the rank-3 and, optionally, camera centers chirality constraints. We employ the Branch-and-Prune paradigm and explore the space of only 5 parameters. Pruning in our method relies on solving Linear Matrix Inequality (LMI) feasibility and Generalized Eigenvalue (GEV) problems that solely depend upon the entries of the DAQ. These LMI and GEV problems are used to rule out branches in the search tree in which a quadric not satisfy- ing the rank and chirality conditions on camera centers is guarantee…

Design of robust observer for T-S fuzzy time-delayed systems subject to unknown inputs

2013

In this paper, a novel approach is proposed to design a robust observer for a class of Takagi-Sugeno (T-S) fuzzy models with unknown inputs and delays. The main contribution of this paper is to consider unknown inputs and a mixed neutral and discrete delay in the model. Also, the system is subject to disturbances, which are imposed on both state and output signals. Delay-dependent sufficient conditions for the design of an unknown input T-S observer with time delays are given in terms of linear matrix inequalities (LMIs). Some relaxations are introduced by using intermediate variables. A numerical example is given to illustrate the effectiveness of the given results.

2014

This paper deals with the problem of robust model predictive control (RMPC) for a class of linear time-varying systems with constraints and data losses. We take the polytopic uncertainties into account to describe the uncertain systems. First, we design a robust state observer by using the linear matrix inequality (LMI) constraints so that the original system state can be tracked. Second, the MPC gain is calculated by minimizing the upper bound of infinite horizon robust performance objective in terms of linear matrix inequality conditions. The method of robust MPC and state observer design is illustrated by a numerical example.

Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps

2014

Abstract This paper investigates the problem of robust finite-time H ∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H ∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H ∞ stabilization using a fuzzy s…