Abstract
This chapter considers the problem of global stabilization of discrete-time time-varying linear systems with input delays and the problem of semi-global stabilization of discrete-time time-varying linear systems with both input delays and magnitude (energy) saturation. The TPF design for continuous-time linear time-delay systems is generalized to the discrete-time setting. For linear systems with both single input delay and multiple input delays, state feedback controls laws using only the current states are constructed to solve these problems. A method for determining the exact condition such that the closed-loop system is asymptotically stable is also proposed if the systems are time-invariant. Moreover, in the situation that the delays in the system are time-varying or even unknown, a delay-independent TPF is also constructed to solve these problems.
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