H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities

Shin, JaeWook; Park, Bum Yong

doi:10.1007/s12555-018-0672-y

Cited by 10 publications

(12 citation statements)

References 24 publications

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“…Therefore, quantized inputs for the analysis and synthesis of control systems have been widely investigated [38]- [43], as they can degrade the performance and stability of modern control systems. Recently, some studies have addressed the stabilization problem of MJSs with quantized inputs [44]- [47]. The stabilization problem for discrete-time MJSs with a quantized feedback input was introduced in [44].…”

Section: Introductionmentioning

confidence: 99%

“…The authors of [46] developed a sliding mode controller for MJSs with a dynamical uniform quantizer and a static logarithm quantizer. Furthermore, an H ∞ controller was proposed for MJSs with quantized input, where known and unknown transition rates were addressed [47]. The above literature assumed that the transition probabilities in MJSs are exactly known or partially known, which is motivativation for this study.…”

Section: Introductionmentioning

confidence: 99%

“…Although the stability analysis and synthesis of MJS with generally uncertain transition rates have been proposed in [32], [33], the authors have only considered an ideal control input without considering quantization. Furthermore, although incomplete transition rates have been employed previously [45], [47], the researchers assumed that some transition rates were known.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Lee

Park

2021

IEEE Access

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This study addresses the stabilization condition for Markovian jump systems with quantized input and generally uncertain transition rates. To stabilize Markovian jump systems with nonlinear inputs using only partial knowledge regarding to the transition rates, the proposed controller is designed as two control parts: a linear control part for stabilizing the system and a nonlinear control part for eliminating undesirable effects from the quantized input. Moreover, an appropriate weighting method, using lower and upper bounds of the partial transition rate, is employed to derive a less conservative stability condition. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed controller.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Lee

Park

2021

IEEE Access

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“…Normally, the elements of the transition probability matrix are assumed to be fully known [14,15]. However, in some practical cases, the transition probabilities may not be fully known, which inspired scholars to study Markov jump systems with partial probability [27][28][29][30][31][32][33][34][35][36][37]. For instance, Zhang and Boukas considered stability and stabilization of Markovian jump systems with partially unknown transition probabilities [27].…”

Section: Introductionmentioning

confidence: 99%

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

Kang

Wang

Hou

2020

Mathematical Problems in Engineering

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This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.

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“…us, recent studies on controller synthesis have focused on MJSs with incomplete knowledge of transition probabilities. Such studies have employed the free-connection weighting method and linear matrix inequalities (LMIs) [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

$H_{2}$ Control of Markovian Jump Systems with Input Saturation and Incomplete Knowledge of Transition Probabilities

Park

2020

Mathematical Problems in Engineering

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This paper proposes an ℋ 2 state-feedback controller for Markovian jump systems with input saturation and incomplete knowledge of transition probabilities. The proposed controller is developed using second-order matrix polynomials of an incomplete transition rate to derive less conservative stabilization conditions. The proposed controller not only guarantees ℋ 2 performance but also rejects matched disturbances. The effectiveness of the proposed method is demonstrated using three numerical examples.

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H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities

Cited by 10 publications

References 24 publications

Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

$H_{2}$ Control of Markovian Jump Systems with Input Saturation and Incomplete Knowledge of Transition Probabilities

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H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities

Cited by 10 publications

References 24 publications

Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Stabilization of Markovian Jump Systems With Quantized Input and Generally Uncertain Transition Rates

Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

H 2 Control of Markovian Jump Systems with Input Saturation and Incomplete Knowledge of Transition Probabilities

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$H_{2}$ Control of Markovian Jump Systems with Input Saturation and Incomplete Knowledge of Transition Probabilities