Abstract
This paper considers the stabilization problem of continuous-time Markovian jump systems (MJSs) by applying a new controller. Different from the traditional methods, a kind of controller experiencing stochastically unmatched modes is proposed. More importantly, its mismatching property is modeled by a stochastically conditional probability and quantized by a given transition probability density function (PDF). Based on the proposed model, more general but less conservative results are presented in terms of linear matrix inequalities (LMIs). Then, some extensions about the expectation of truncated PDF matrix uncertain, partially known and nonsingular respectively are further considered. Finally, a practical example is used to illustrate the effectiveness and superiority of the developed theoretical results.
Highlights
INTRODUCTIONMarkovian jump system (MJS) is a special kind of hybrid systems. It is very suitable to describe dynamic systems affected by environmental factors and abrupt changes in internal structural parameters
As we know, Markovian jump system (MJS) is a special kind of hybrid systems
The main contributions of this paper are summarized as follows: 1) A kind of controller is proposed to realize the stabilization aim, whose operation mode is not synchronous with others but stochastically unmatched; 2) Because of a stochastically conditional probability exploited and quantized, less conservative results are obtained with linear matrix inequalities (LMIs) forms and more general than existing ones; 3) They are further extended to more general cases that the expectation of truncated probability density function (PDF) matrix is uncertain, partially known and nonsingular respectively
Summary
Markovian jump system (MJS) is a special kind of hybrid systems. It is very suitable to describe dynamic systems affected by environmental factors and abrupt changes in internal structural parameters. In networked control systems (NCSs), since the network-induced delay, congestion and limited communication inevitably occur, such a probability is impossible to be constant. When it is varied, how to consider the similar problems? The main contributions of this paper are summarized as follows: 1) A kind of controller is proposed to realize the stabilization aim, whose operation mode is not synchronous with others but stochastically unmatched; 2) Because of a stochastically conditional probability exploited and quantized, less conservative results are obtained with LMI forms and more general than existing ones; 3) They are further extended to more general cases that the expectation of truncated PDF matrix is uncertain, partially known and nonsingular respectively. We use ‘‘∗’’ as an ellipsis for the terms induced by symmetry, diag {· · ·} for a block-diagonal matrix, and (M ) M + M T
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