Furthermore, input-to-state practical stability for the proposed control strategy is guaranteed under certain conditions.
(ii) We introduce the concept of Jump Input-to-State practical Stability (JISpS) and give stochastic Lyapunov stability criterion.
First, an appropriate reference signal is designed such that the internal dynamic subsystem is input-to-state practical stable.
In particular, we show that the closed-loop system is input-to-state practical stable (ISpS) in the attraction region at triggering time instants.
Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward.
Then, with the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem extending to the stochastic case, together with DSC design technique, an adaptive neural network (NN) output feedback controller is proposed.
With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem being extended to stochastic case, by combining stochastic small-gain theorem with backstepping design technique, an adaptive output-feedback controller is proposed.
With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem extended to the stochastic case, together with the RBF NN technique, an adaptive NN output feedback controller is proposed.
At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract modelling errors is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptions are introduced to reduce the ultimate error bound.
Indeed, as John Maynard Keynes once stated, "Practical men, who believe themselves to be quite exempt from any intellectual influences, are usually the slaves of some defunct economist".
None of these machines was a computer, but they did advance the state of practical mechanical knowledge knowledge that would be used in computers later.
