Direct adaptive control for linear discrete-time uncertain systems with exogenous disturbances and /spl lscr//sub 2/ disturbances

Direct Adaptive Feedback Design for Linear Discrete‐time Uncertain Systems

“…Nevertheless, the synthesis and stability analysis of discrete event systems in [11,12] and the algebraic results given in [10,13] motivate us to apply Lyapunov concepts in the discrete-time adaptive feedback control scheme. We also extend the results from [14,15] to a system without the restriction imposed by the reachability hypothesis.…”

“…Specifically, they can be involving the dynamic control of vehicles while fuel consumption is unknown, the precision control when system parameters are uncertain, etc. Interested reader may refer to the aircraft control example given in [14,15]. The efficacy of the proposed framework is demonstrated by two numerical examples provided at the end of this paper.…”

“…It is worth noting that the direct adaptive stabilizing framework developed in this paper is distinct from the existing results. With the results from [14,15], our framework can be easily applied to systems in which the bound on the uncertainties is known. Specifically, they can be involving the dynamic control of vehicles while fuel consumption is unknown, the precision control when system parameters are uncertain, etc.…”

“…thermore, let R > 0, and let n n P × ∈ be a positive definite solution to the Lyapunov equation (4). The fractored update law, denoted by K(k) = | B s | K(k), k > 0, and given by (15) guarantees that the closed-loop system described by (1), (5), and (15)…”

“…The result of Corollary 2.1 can be directly applied to the class of system (1) where uncertainties exist in both the system and input matrices. The update law of the feedback gain given in (15) is factored by a positive and symmetric matrix | B s |. The implies that the closedloop solution of (1), (5), and (15) becomes…”