Abstract
The guaranteed cost control problem for a class of nonlinear discrete time-delay systems is investigated. Based on the Lyapunov matrix, a complete-type Lyapunov-Krasovskii functional is constructed. Thereby, the Lyapunov stability theory is employed to design the exact form of the controller to ensure that the resultant closed-loop system is asymptotically stable and the cost function is bounded. A numerical example is presented to illustrate the usefulness of the theoretical results.
Highlights
As is well known, time delays frequently occur in various practical systems and often result in poor performance and/or instability
Motivated by [32] and [33], this paper studies the guaranteed cost control problem for a class of nonlinear discrete time-delay systems by proposing a Lyapunov matrix method
We construct a complete-type Lyapunov–Krasovskii functional based on the Lyapunov matrix
Summary
Time delays frequently occur in various practical systems and often result in poor performance and/or instability. Motivated by [32] and [33], this paper studies the guaranteed cost control problem for a class of nonlinear discrete time-delay systems by proposing a Lyapunov matrix method. The main contributions of this paper can be summarised as follows: (i) based on the Lyapunov matrix, a completetype Lyapunov–Krasovskii functional is constructed, which is different form the most existing ones; (ii) a sufficient condition for the existence of state-feedback guaranteed cost controller is derived; (iii) an explicit guaranteed cost controller is designed such that the closed-loop system is asymptotically stable as well as a specific quadratic cost function has an upper bound, and an explicit expression of the controller is given. AT denotes the transpose of matrix A. ∗ in a matrix represents the elements below the main diagonal of a symmetric matrix
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