Stabilizing controllers using observers for uncertain systems with delays

Observer-based sliding mode control for a class of discrete systems via delta operator approach

“…From Definition 1 the closed-loop system (14) and (17) is asymptotically stable in delta domain. This completes the proof.…”

“…The following theorem gives a sufficient condition for asymptotic stability of the overall closed-loop system which composes of state estimate dynamics (14) and state estimation error dynamics (17). …”

“…Furthermore, the state observer design problem has been also paid considerable attention at the same time, for examples [13][14][15], an observer was designed for discrete-time uncertain nonlinear systems with time delays [16]. A robust non-fragile H 1 observer-based control was investigated for continuous-time delayed systems [17].…”

“…The combined closed-loop system which composes of state estimate dynamics(14) and state estimation error dynamics(17)is asymptotically stable, if there exist matrices Y, N, X 40, and scalars e 1 40, e 2 40, e 3 40 and e 4 40 satisfying…”

Robust observers for neutral jumping systems with uncertain information

“…On the other hand, robust observation (or estimation) [5,26,9,28,30] is concerned with the state reconstruction when the plant model has uncertain parameters and is described by ordinary differential equations (ODE) or equivalent representation. Following the third approach based on FDS, results on estimating the state of uncertain system with statedelay are developed in [18] and related work can be found in [21]. An integral part of FDS [11][12][13]32] is the class of neutral-type systems which can be found in several applications including, but not limited to, chemical reactor, rolling mill, infeed grinding, lossless transmission lines and hydraulic systems.…”