linear matrix inequality

摘要： This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

摘要： This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

摘要： In this paper, the problem of delay-dependent sta- bility criteria for a class of constant time-delay neutral systems with time-varying structured uncertainties is investigated. New asymptotic stability criteria are derived in the form of linear ma- trix inequality. Two numerical examples are given to indicate that the results presented in this paper are effective and less conservative than some existing results.

摘要： The problem of roust stabilization for linear time-varying uncertain periodic descriptor systems is revisited. Based on the concept of robust stability for linear time-varying uncer-tain periodic descriptor systems, a necessary and sufficient con-dition for robust stability is put forward. The robust stabiliza-tion problem is also studied and the corresponding necessary and sufficient condition is given using the notation of dual system.The obtained matrix inequality conditions can be transformed to linear matrix inequality ones with the introduction of some free matrices, which makes the analysis and design procedure simple and reliable.

摘要： Based on the linear matrix inequality (LMI)method, this paper discusses the impulse dissipative problem for a class of singular systems with uncertainties under the description of state-space, and obtains the robust impulse dissipative state feedback controller and output feedback controller for singular systems with allowable uncertainties by solving the linear matrix inequalities. At last, we testify the feasibility of our results by a numerical example.

摘要： This paper considers the problem of delay-dependent robust stabilization for uncertain singular delay systems. In terms of linear matrix inequality (LMI) approach, a delay-dependent stability criterion is given to ensure that the nominal system is regular, impulse free, and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free, and stable for all admissible uncertainties. An explicit expression for the desired controller is also given. Some numerical examples are provided to illustrate the validity of the proposed methods.

摘要： This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discretedelay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.

摘要： This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno (T-S) model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality (LMI) approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.

摘要： The robust stability of a class of Hopfield neural networks with multiple delays and parameter perturbations is analyzed. The sufficient conditions for the global robust stability of equilibrium point are given by way of constructing a suitable Lyapunov functional. The conditions take the form of linear matrix inequality (LMI), so they are computable and verifiable efficiently.Furthermore, all the results are obtained without assuming the differentiability and monotonicity of activation functions. From the viewpoint of system analysis, our results provide sufficient conditions for the global robust stability in a manner that they specify the size of perturbation that Hopfield neural networks can endure when the structure of the network is given. On the other hand, from the viewpoint of system synthesis, our results can answer how to choose the parameters of neural networks to endure a given perturbation.

摘要： A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.

摘要： The robust fault detection filter (RFDF)design problems are studied for linear singular time-delaysystems with both exogenous disturbances and parameter uncertainties. Firstly，appropriate input/output selectionmatrices are introduced to extend a performance index to the time-delay systems in time domain. Then applyingrobust H∞ optimization control technique，the RFDF system is not only regular，impulse free and stable，but alsomeets an H∞-norm bound constraint on disturbance attenuation. The existence conditions of the robust faultdetection filter for linear singular time-delay systems with both exogenous disturbances and parameteruncertainties are presented in terms of linear matrix inequality (LMI)formulation，independently of time delay.