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The purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

The authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions.

It turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results.

The novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

This paper aims to propose a new linear parameter varying (LPV) controller for the robot tracking control problem. Using the identification of the robot dynamics in different work space points about modeling trajectory based on the least square of error algorithm, an LPV model for the robotic arm is extracted.

Parameter set mapping based on parameter component analysis results in a reduced polytopic LPV model that reduces the complexity of the implementation. An approximation of the required torque is computed based on the reduced LPV models. The state-feedback gain of each zone is computed by solving some linear matrix inequalities (LMIs) to sufficiently decrease the time derivative of a Lyapunov function. A novel smoothing method is used for the proposed controller to switch properly in the borders of the zones.

The polytopic set of the resulting gains creates the smooth switching polytopic LPV (SS-LPV) controller which is applied to the trajectory tracking problem of the six-degree-of-freedom PUMA 560 robotic arm. A sufficient condition ensures that the proposed controller stabilizes the polytopic LPV system against the torque estimation error.

Smoothing of the switching LPV controller is performed by defining some tolerances and creating some quasi-zones in the borders of the main zones leading to the compressed main zones. The proposed torque estimation is not a model-based technique; so the model variation and other disturbances cannot destroy the performance of the suggested controller. The proposed control scheme does not have any considerable computational load, because the control gains are obtained offline by solving some LMIs, and the torque computation is done online by a simple polytopic-based equation.

In this paper, a new SS-LPV controller is addressed for the trajectory tracking problem of robotic arms. Robot workspace is zoned into some main zones in such a way that the number of models in each zone is almost equal. Data obtained from the modeling trajectory is used to design the state-feedback control gain.

This paper aims to present a simplified method to analyze the transient characteristics of a fractional-order very high frequency (VHF) resonant boost converter. The transient analytical solutions of state variables obtained by this method could be used as a guide for parameter design and circuit optimization.

The VHF converter is decoupled into a simplified equivalent circuit model and described by the differential equation. The solution of the simplified equivalent circuit model is taken as the main oscillation component of the transient state variable. And the equivalent small parameter method (ESPM) and Kalman filter technology are used to solve the differential equation of the converter to obtain the steady-state ripple component. Then, by superimposing the abovementioned two parts, the approximate transient analytical solution can be acquired. Finally, the influence of the fractional order of the energy storage elements on the transient process of the converter is discussed.

The results from the proposed method agree well with those from simulations, which indicates that the proposed method can effectively analyze the transient characteristic of the fractional-order VHF converter, and the analytical solution derived from the proposed mathematical model shows sufficient accuracy.

This paper proposes for the first time a method to analyze the transient characteristics of a fractional-order VHF resonant boost converter. By combining the main oscillated solution derived from the simplified equivalent circuit model with the steady-state solution based on ESPM, this method can greatly reduce the computation amount to estimate the transient solution. In addition, the discussion on the order of fractional calculus of energy storage components can provide an auxiliary guidance for the selection of circuit parameters and the study of stability.