Abstract
This paper considers the robust finite-time stabilization problem for a class of discrete-time linear singular systems with norm-bounded parameter uncertainties. With the introduction of an additional matrix to describe the algebraic relationship between the slow subsystem and fast subsystem of a discrete-time linear singular system, a matrix inequality condition is first given for a discrete-time linear singular system to be regular, causal and finite-time stable. With this condition, the robust finite-time stability and robust finite-time stabilization problems are also resolved, and the explicit expression of the desired state feedback control law is also given in terms of a set of matrix inequalities. A numerical example is given to show the effectiveness of the proposed method.
Highlights
IN many practical applications, the main concern of the system behavior is focused in a finite time interval, which is different from the traditional Lyapunov stability since it performance is defined over an infinite time interval
The missile attitude control system is only defined in the time interval between its launch time and the time hitting the target, and the dynamic performance in a short time interval is more preferred for the automotive suspension control system
It is said to be finite-time stable if its state does not exceed a certain threshold during a specified time interval when the bound on the initial condition is given prior [4]
Summary
IN many practical applications, the main concern of the system behavior is focused in a finite time interval, which is different from the traditional Lyapunov stability since it performance is defined over an infinite time interval. The finite-time observer design problem was considered recently for a class of singular systems subject to unknown inputs in both the state and the output equations in [14], where some linear matrix inequality results were given. For discrete-time linear singular systems, the finite-time stability analysis problem was first studied in [15], where the matrix norm approach was used to derive sufficient conditions for finite-time stability. This condition is further formulated in terms of strict matrix inequalities Based on this condition, the robust finite-time stabilization problem is resolved, and the explicit expression of the desired state feedback control law is given in terms of a set of matrix inequalities. 2) A strict matrix inequality condition is given for the state feedback control law design such that the resultant closed-loop system to be regular, causal and finite-time stable for all admissible uncertainties. We here highlight that the obtained criteria are formulated in terms of strict matrix inequalities, which has some mathematical elegance and comparatively easy to be versified numerically
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