In the previous work, the authors studied the problem of robust discretization of linear time-invariant systems with polytopic uncertainties, where linear matrix inequality (LMI) conditions were developed to find an approximate discrete-time (DT) model of a continuous-time (CT) system with uncertainties in polytopic domain. The system matrices of obtained DT model preserved the polytopic struct...

This technical note addresses robust stability of uncertain systems with rational dependence on unknown time-varying parameters constrained in a polytope. First, the technical note proves that a sufficient linear matrix inequality (LMI) condition that we previously proposed, based on homogeneous polynomial Lyapunov functions (HPLFs) and on the introduction of an extended version of Polya’s theo...

Takagi-Sugeno (TS) fuzzy modeling and control techniques are applied to the classical nonlinear Ball and Beam problem. The nonlinear model is segmented to different local linear models. Local controllers are hence designed using LMI theory for achieving a robust control behavior for ball position. TS fuzzy modeling is applied to generate suitable fuzzy models, and the associated controllers. Us...

This paper introduces new dilated LMI conditions for continuous-time linear systems which not only characterize stability and H2 performance specifications, but also, H∞ performance specifications. These new conditions offer, in addition to new analysis tools, synthesis procedures that have the advantages of keeping the controller parameters independent of the Lyapunov matrix and offering suppl...

In this paper a new Linear Matrix Inequality (LMI) based switching controller for multiple Bottleneck packet switching Network has been considered. The main goal is to illustrate the effects of the Switching Control methodology on the congestion control problem of the packet switching Networks with dynamically varying parameters such as Link capacity and time delays. The congestion dynamic for ...

In this paper, we propose new LMI-based conditions for robust stability/performance analysis of linear timeinvariant (LTI) uncertain systems. To get around the conservatism of existing conditions resulting from Lyapunov’s stability theory, we first consider to employ Lyapunov functions that can be associated with higher-order derivatives of the state vectors. This motivates us to introduce a re...

This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the H∞ and H2 model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order n to be reduced to an order r = n/s where n, r, s ∈ N. Arbitrary order of the reduced model can be enforced by including states in the original system with negligible input-to-output...

This paper is concerned with the problem of finding a low-rank solution of an arbitrary sparse linear matrix inequality (LMI). To this end, we map the sparsity of the LMI problem into a graph. We develop a theory relating the rank of the minimum-rank solution of the LMI problem to the sparsity of its underlying graph. Furthermore, we propose three graph-theoretic convex programs to obtain a low...

This paper presents investigations into the development of a linear matrix inequalities (LMI) based robust PID control of a nonlinear Two-Link Flexible Manipulator (TLFM) incorporating payload. A set of linear models of a TLFM is obtained by using system identification method in which the linear model represents the operating ranges of the dynamic system. Thus, the LMI constraints permit to rob...

This paper describes the LMI synthesis of feedback controllers which minimise closed loop transient perturbation growth with limited control effort. Controllers are synthesized for the linearised Lorenz equations, and their performance is compared to that of LQR controllers. At low control effort the controllers behave similarly, but the LMI based controllers are able to produce an almost monot...