In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capabi...
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In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.
This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states. Based on the well-known Fornasini-Marchesini local state-sp...
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This study addresses the robust stabilisation problem for the two-dimensional (2D) discrete non-linear stochastic systems with time-varying delays in states. Based on the well-known Fornasini-Marchesini local state-space model, a more general 2D discrete non-linear system is considered with both stochastic disturbances and time-varying delays. Our attention is focused on the design of a delay-dependent state-feedback controller so that the 2D stochastic non-linear system is guaranteed to be globally asymptotically stabilisable in the mean square. By using the stochastic analysis and some inequality techniques, sufficient criteria ensuring the existence of such controllers are derived in terms of matrix inequalities, which can be effectively solved by resorting to some standard convex optimisation algorithms. Furthermore, such stabilisation results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. Finally, a numerical example is provided to demonstrate the applicability of the proposed controller design approach.
This study deals with the optimal control problem for a class of delta-domain networked control systems (NCSs) subjected to both matched and unmatched disturbances. In the presence of the disturbances, the so-called e...
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This study deals with the optimal control problem for a class of delta-domain networked control systems (NCSs) subjected to both matched and unmatched disturbances. In the presence of the disturbances, the so-called epsilon-optimum is proposed to quantify the control performance. The purpose of the addressed problem is to design the optimal control strategy such that the cost function is minimised over the finite-/infinite-horizon under the network-induced constraints. In virtue of the dynamic programming method, sufficient conditions are established to guarantee the existence of the desired control strategies, and the controller parameters are designed. For the obtained optimal control strategy, an upper bound for the epsilon-optimum is provided explicitly, and convex optimisation algorithms are given to compute such upper bound. Both simulation and experimental results are provided to illustrate the usefulness and applicability of the proposed methods.
This study addresses the stabilisation problem via decentralised controllers for continuous-time positive fractional-order (FO) interconnected systems. By virtue of the positivity, a necessary and sufficient condition...
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This study addresses the stabilisation problem via decentralised controllers for continuous-time positive fractional-order (FO) interconnected systems. By virtue of the positivity, a necessary and sufficient condition is first derived for asymptotic stability of the interconnected closed-loop system. Then, necessary and sufficient conditions for designing a decentralised state-feedback controller are formulated in the form of a linear programming problem which can be effectively solved by using various convex optimisation algorithms. The effectiveness of the obtained theoretical results is demonstrated by a numerical example in positive FO circuits.
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