Stability Analysis of Markovian Jump Systems by Yu Kang Yun-Bo Zhao & Ping Zhao

Author:Yu Kang, Yun-Bo Zhao & Ping Zhao
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

4.2 Description of Nonlinear Uncertain Jump System

Consider the following piecewise nonlinear uncertain jump system :

(4.1)

where is the state vector, is the control input. The parameter is continuous-time Markov process on the probability space which takes values in the finite discrete state-space with generator given by

(4.2)

where

is the transition rate from i to j, and

and is assumed to be exactly known at each time.

The functions with , and are smooth functions of x(t) for each value of such that the system (4.1) is well defined, that is, the only equilibrium point of the system (4.1) is for any initial state and any admissible control u(t), where denotes all functions on which are infinitely continuously differentiable in x(t) for each .

We have the following simplified assumptions.

Assumption 4.1

The matrix-valued function is continuous at , and it satisfies the linear growth condition as follows:

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