Stabilization and Exponential Estimation of Linear Discrete-Time Systems with Input and State Delays Base on a Novel Controller Design Approach

This paper is concerned with two problems for linear discrete-time systems with input and state delays. The first one is to design a stabilization controller. Anther one is to give the exponential estimation of the closed-loop systems. To this and, we first define matrices and use them to represent the state of the system, and then give the concrete expression of the novel controller. Secondly, define a Lyapunov matrix and construct a Lyapunov-Krasovskii functional. At the same time, the upper and lower bounds of this Lyapunov-Krasovskii functional will be given. Thereby, by employing Lyapunov-Krasovskii functional approach, the exponential estimation of the closed-loop systems is obtained. Finally, two numerical examples illustrate the validity of the conclusion.