Stability analysis of random nonlinear systems with time-varying delay and its application

Abstract

This paper studies a class of random nonlinear systems with time-varying delay, in which the r-order moment (r ≥ 1) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear timedelay systems. Secondly, some definitions and criteria on noiseto-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, two regulation controllers are constructed respectively for two corresponding random nonlinear time-delay systems and the effectiveness of two proposed recursive procedures are demonstrated by two simulation examples.

Dynamic Analysis of a Chaotic 3d Quadratic System Using Planar Projection.

“…In this section we will give the explicit formulas to determine the direction, stability and period of these periodic bifurcation solutions at point E for the critical value a 1 = a 0 , using regular form techniques [1] , [9] , [14].…”

Stability criteria of random delay differential systems subject to random impulses

“…Under Assumption A1, it can be checked from References 31, 32, and 35 that there is a unique global solution over . Thus we omit the proof of the unique global solution for system (1) here.…”

“…The highlights of this article lie in the following aspects: For the continuous dynamics of the impulsive systems, the nonlinear systems with the time‐delay and random disturbances driven by the second‐order moment processes are considered. The second‐order moment process is more suitable than the white noise to describe the random disturbance in the practical models 17,32 and have wide applications in engineering 18,33 The impulsive intensity in the discrete dynamics is a series of random variables, and the kind is determined by two different kinds of random characterizations, an arbitrary random sequence and an irreducible aperiodic Markov chain, which are more realistic and challenging than that in Reference 31 and other deterministic cases in References 24 and 27. The definitions and the criteria of global asymptotic stability in probability and exponential stability in th moment are proposed for random delay differential systems subject to random impulses, which can be regarded as the natural extensions of References 17,31, and 32 for random nonlinear systems in terms of random impulse effects.…”

Practical trajectory tracking of output constrained random nonlinear systems

“…More recently, a feasible scheme in disposing the practical trajectory tracking of random Lagrange system was provided in Reference 38. Further in‐depth studies on random nonlinear systems were discussed in References 39‐45. It is worth noting the fact that results currently are inapplicable to the trajectory tracking of output constrained random nonlinear systems.…”