Nima Yeganefar

Finite-time stability and stabilization of time-delay systems

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artsteins model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.

Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability

This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability.

Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability

The main contribution of this technical note is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Liapunov-Krasovskii methodology. It is proved that a system which is (globally, locally) exponentially stable in the unforced case is (globally, locally) input-to-state stable when it is forced by a measurable and locally essentially bounded input, provided that the functional describing the dynamics in the unforced case is (globally, on bounded sets) Lipschitz and the functional describing the dynamics in the forced case satisfies a Lipschitz-like hypothesis with respect to the input. Moreover, a new feedback control law is provided for delay-free linearizable and stabilizable time-delay systems, whose dynamics is described by locally Lipschitz functionals, by which the closed-loop system is ISS with respect to disturbances adding to the control law, a typical problem due to actuator errors.

LMI Stability Conditions for 2D Roesser Models

This note is devoted to the stability analysis of linear two-dimensional systems described by continuous, discrete or mixed Roesser models. Commonly used polynomial-based tests of stability are reduced to that of solving a set of linear matrix inequalities. The main contribution is that the approach is very general and the criteria, under certain hypothesis, are not conservative.

Robust stability of hybrid Roesser models against parametric uncertainty: a general approach

This paper aims at proposing a general framework for the establishement of LMI conditions to analyse the robust stability of a singular hybrid Roesser model subject to parametric uncertainties. The uncertain parameters are involved through implicit Linear Fractional Representations (LFR). Special focus is put on the influence of the number of uncertain parameters and the dimensionality of the model. More precisely it is shown that each dimension can nearly be regarded as an uncertain parameter and the other way around. Therefore, their influence on the conservatism of the obtained condition is very similar.

Structural stabilization of linear 2D discrete systems using equivalence transformations

We consider stability and stabilization issues for linear two-dimensional (2D) discrete systems. We give a general definition of structural stability for all linear 2D discrete systems which coincides with the existing definitions in the particular cases of the classical Roesser and Fornasini–Marchesini discrete models. We study the preservation of the structural stability by equivalence transformations in the sense of the algebraic analysis approach to linear systems theory. This allows us to use recent works both on the stabilization of linear 2D Roesser models and on the equivalence of linear multidimensional systems in order to develop a stabilization method for linear 2D discrete Fornasini–Marchesini models.

Input-to-State Stability and exponential stability for time-delay systems: further results

The main contribution of this paper is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Liapunov-Krasovskii methodology. It is proved that a system which is (globally, locally) exponentially stable in the unforced case is (globally, locally) input-to-state stable when it is forced by a measurable and locally essentially bounded input, provided that the functional describing the dynamics in the unforced case is (globally, on bounded sets) Lipschitz and the functional describing the dynamics in the forced case satisfies a Lipschitz-like hypothesis with respect to the input. Moreover, a new feedback control law is provided for delay-free linearizable and stabilizable time-delay systems, whose dynamics is described by locally Lipschitz functionals, by which the closed loop system is ISS with respect to disturbances adding to the control law, a typical problem due to actuator errors.

On Stabilization of 2D Roesser Models

This note is devoted to the stabilization of 2D Roesser models which are discrete, continuous, or mixed continuous-discrete. A recent linear matrix inequalities (LMIs) necessary and sufficient condition for stability of such models is used to derive a quasi non conservative technique for state feedback stabilization.

H ∞ Performance Analysis of 2D Continuous Time-Varying Delay Systems

This paper deals with the problem of