On the state observation and output feedback problems for nonlinear uncertain dynamic systems

Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

“…Letting the observation error be defined as (t) =x(t) − x(t), the form of o(x, y, t) (nonlinear adaptive gain) can be defined similarly as in [3]:…”

“…In this work (the preliminary results are presented in [18]), we address the design of a nonlinear robust observer, which is used to estimate the missing velocity signal for the nonlinear PKM dynamics system and has an additional term similar to [3] that is used to guarantee robustness against nonlinearities and/or uncertainties in the system model and external disturbances. Then, the estimated velocity, along with the gravitation compensation, dynamic friction and external disturbance compensation for the PKM, are used to design a PD controller in order to solve the position control problem.…”

The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

“…Therefore, the synchronization method at exponential rate has become a topic worthy of study. The main work at present that has been done in this area is in the following aspects: On the basis of certain assumptions, a synchronization method based on state observer is proposed by the thesis [14]. For a class of uncertain nonlinear systems, the paper [15] proposed a nonlinear feedback control method with good robustness; The paper [16] presented a new method of nonlinear feedback exponential stable synchronization based on the boundedness of chaotic system.…”

Bounded Controllers for Uncertain Nonlinear Systems

“…For uncertain systems with linear nominal part, the problem of state observation was considered in [5] and [14], sufficient conditions for the existence of an output feedback stabilizing controller were given in [1] and [5], stabilizing bounded controllers were proposed in [2], [3], [4], [6], [7], [10], [11], [13].…”