In this paper, the exponential stability of singularly perturbed discrete systems (SPDSs) with time-delay is investigated via the Lyapunov’s direct method. In the previous results about the SPDS with time-delay, the asymptotic stability is obtained using the frequency-domain approach. However, we propose a composite Lyapunov function to show that the SPDS with time-delay is exponentially stable...

In this paper, we consider Lur’e type differential-algebraic systems (LDS) and introduce the concept of strongly absolute stability. Such a notion is a generalization of absolute stability for Lur’e type standard state-space systems (LSS). By a Lur’e type Lyapunov function, we derive an LMI based stability criterion for LDS to be strongly absolutely stable. Using extended strictly positive real...

Abstract: In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to parameterize functionals which are positive or negative on certain function spaces. Applying this parameterization to construct Lyapunov functionals wi...

This paper is concerned with the mixed H2/H∞ control problem combined with robust pole placement in linear matrix inequality (LMI) regions. Based on Differential Evolution algorithms (DEs), Salomon’s Evolutionary Gradient Search method (EGS) and LMIs, a hybrid algorithm is presented for numerical computation of a robust fixed-order, static or dynamic, output feedback controller. This approach d...

The Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. ...

We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design speciications include robust stability, robust performance (H 2-norm) bounds and time-domain bounds (output and command input peak). We derive suucient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the cl...

In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria i...

A sufficient condition for the robust D-stability of dynamic interval systems is proposed in this paper. This D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of matrix inequalities defined at a series of partialvertex-based interval matrices other than the total vertex matrices as previous results. This condition is also extended ...

In this paper new necessary and sufficient conditions for static output feedback robust controller design for linear discrete timeinvariant systems have been used. The output feedback robust controller design may be reduced to the problem of finding a feasible point under Biaffine Matrix Inequality constraint. In this paper the BMI problem of the output feedback robust controller design has bee...

In this note we consider the problem of state feedback stabilization of a class of nonlinear discrete-time delay systems. From an appropriate Lyapunov function and judicious mathematical manipulations, we deduce a simple LMI condition (that may be checked easily) to ensure asymptotic stabilization. On the other hand, we provide two explicit state feedback laws that may be seen as a generalizati...