Sreten B. Stojanovic

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Large Scale Time Delay Autonomous Systems

This paper offers new, necessary and sufficient conditions for delay–dependent asymptotic stability of the linear discrete large scale time delay systems. It has been shown that asymptotic stability this class of systems can be mapped to the asymptotic stability of the corresponding so called ith discrete SES systems. The order of the SES system is manifold lower than the order of the observed large scale systems. At that, it necessary to solve system of matrix equations whose solution always exists. Using the feature that the observed large scale system is finite-dimensional, necessary and sufficient condition of stability was derived independent of time-delay, which is based on the equivalent matrix of the system, whose order is considerably higher than the corresponding SES system. Numerical computations are presented for illustration.Copyright

Singular Time Delayed System Stability Theory in the sense of Lyapunov: A Quite New Approach

This paper gives sufficient conditions for the stability of linear singular continuous delay systems of the form Ex(t)=Aox(t) + A1x.(t-tau}. These new, delay-independent conditions are derived using approach based on Lyapunovs direct method. A numerical example has been working out to show the applicability of results derived.

Stability of singular time-delay systems in the sense of non-Lyapunov: Classical and modern approach

This paper provides sufficient conditions for both practical stability and finite-time stability of linear singular continuous time-delay systems which can be mathematically described as Ex(t)=Aox(t)+A1x(t-t). Considering a finite-time stability concept, new delay independent and delay dependent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior. Moreover an linear matrix inequality (LMI) approach has been applied in order to get less conservative conditions.

Further results on singular time delayed system stability

This paper gives sufficient conditions for the stability of linear singular continuous delay systems of the form Ex(t) = A/sub 0/x(t) + A/sub 1/x(t - T). These new, delay-independent conditions are derived using approach based on Lyapunovs direct method.

Stability of linear discrete time delay systems: Lyapunov-Krasovskii approach

This paper gives a new Lyapunov-Krasovskii method for discrete time delay systems. Based on the method, new delay-independent conditions are derived. A numerical example has been working out to show the applicability of results derived.

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

Abstract This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form x ( k +1) = A 0 x ( k ) + A 1 x ( k – h ). The time-dependent criteria are derived by Lyapunovs direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditions of convergence of Traub and Bernoulli algorithms for computing the dominant solvent of the matrix polynomial equation are derived. Numerical computations are performed to illustrate the results obtained.

Lyapunov stability theory: a quite new approach - discrete descriptive time delayed system

This paper gives sufficient conditions for the stability of linear singular discrete delay systems of the form Ex(k + 1) = A0x(k) + A1x(k - 1). These new, delay-independent sufficient conditions are derived using approach based on Lyapunovs direct method. A numerical example has been working out to show the applicability of results derived

Exponential Stability of Discrete Time Delay Systems With Nonlinear Perturbations

This paper gives sufficient condition for the exponential stability of discrete delay systems with nonlinear perturbations. This new, delay–dependent condition is derived using approach based on Lyapunov’s direct method. A numerical example has been working out to show the applicability of results derived.Copyright

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

Abstract The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.

New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.