Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation

Abstract

Summary This paper proposes less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation. The transition rates associated with the transition probabilities are expressed in terms of three properties, which do not require the lower and upper bounds of the transition rates, differently from other approaches in the literature. The resulting conditions are converted into the second‐order matrix polynomial of the unknown transition rates. The polynomial can be represented as quadratic form of vectorized identity matrices scaled by one and the unknown transition rates. And then, the LMI conditions are obtained from the quadratic form. Also, an optimization problem is formulated to find the largest estimate of the domain of attraction in mean square sense of the closed‐loop systems. Finally, two numerical examples are provided to illustrate the effectiveness of the derived stabilization conditions. Copyright © 2016 John Wiley & Sons, Ltd.

Non‐Fragile Simultaneous Actuator and Sensor Fault‐Tolerant Control Design for Markovian Jump Systems Based on Adaptive Observer

“…In this section, a practical example will be provided to show the effectiveness of the proposed approach. Consider the following system , where the nominal system matrix A ( t ) is taken from the linearized model of an F‐404 aircraft engine system in β ( t ) is an unknown parameter. Let β ( t ) be subjected to a Markov process r ( t ) with s =2, and the TRM is assumed to be .…”

“…Thus they have received much attention over the past few decades. Many important results have been reported on the issues of stability, stabilization, feedback control and filtering with respect to MJSs , but very few results have been made on the fault estimation and FTC problems . For example, considered the stabilization of MJSs against input disturbances, as well as the actuator and sensor faults, which were estimated by an augmented sliding mode observer.…”

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

“…Because of two kinds of mechanisms contained, it is very suitable to model such actual systems whose structures or parameters change [1,2]. Over the past years, many research topics on MJSs have been extensively studied, like stability analysis [3][4][5][6], stabilization [7][8][9][10][11], robust control [12][13][14][15], adaptive control [16][17][18][19], ∞ filtering and control [20,21], state estimation [22][23][24][25], synchronization [26][27][28][29][30], and so on.…”

Robust Control for Discrete-Time Singular Marovian Jump Systems with Partly Unknown Transition Rates

“…But, the results developed in these references require the critical assumption on the complete knowledge of the transition probabilities in the jump process, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. [26] proposes the less conservative stabilization conditions for MJSs with incomplete knowledge of transition probabilities and input saturation. The delay-dependent stability problem for neutral Markovian jump systems with generally unknown transition rates was investigated in [27].…”