Class Of Uncertain Discrete-time Systems Research Articles

Guaranteed cost stabilization for a class of uncertain discrete-time systems

A technique to design stabilizing state feedback controllers is presented for a class of linear discrete-time systems subject to possibly time-varying uncertainties that affect the system and input matrices. The controller design procedure is based on the solution of one of three modified algebraic Riccati matrix equations. Stability considerations rely on the second method of Lyapunov. To evaluate the system's performance degradation due to uncertainly, an upper bound (guaranteed cost) is derived for the cost of the controlled uncertain system with respect to a designer-chosen quadratic cost function. An example adapted from the literature is used to illustrate the method.

Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty

This paper presents an algorithm for the stabilization of a class of discrete-time uncertain systems suffering from uncertainty of the norm bounded time varying type. The stabilizing control gain matrix is obtained by solving a certain discrete Riccati equation. The solution of this Riccati equation is also a Lyapunov matrix which is used to establish the stability of closed-loop system. The results presented in this paper generalize those obtained in previous works for continuous-time uncertain systems.