Stability Of Discrete-time Uncertain Systems Research Articles

Stability of discrete-time uncertain systems with a time-varying state delay

The stability analysis problem for unforced discrete-time systems with a time-varying state delay is considered. Stability criteria for nominal and uncertain system models are derived such that the upper and lower bounds on the delay time can be determined to ensure asymptotic stability. There is no need to assume that the system is stable when the delay vanishes. Adopting the linear matrix inequality approach enables the computations to be implemented conveniently. Compared with existing results in the literature, the proposed method is less conservative for many cases.

A new LMI condition for robust stability of discrete-time uncertain systems

In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.

A less conservative LMI condition for the robust stability of discrete-time uncertain systems

In this paper, a less conservative condition for the robust stability of uncertain discrete-time linear systems is proposed. The uncertain parameters, assumed to be time-invariant, are supposed to belong to convex bounded domains (polytope type uncertainty). The stability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain. A simple and numerically efficient feasibility test provides a set of Lyapunov matrices whose convex combination can be used to assess the stability of any dynamic matrix inside the uncertainty domain. Examples illustrate the results.