Reliable H//sub∞/ aircraft flight controller design against faults with state/output feedback

In this paper, we are concerned with H ∞ model reduction of 2-D discrete systems in Roesser model. For positive 2-D discrete systems, the aim is to construct a positive 2-D reduced-order system such that the error system satisfies a prescribed H ∞ norm bound constraint. Based on a system augmentation approach, a new sufficient condition is proposed to ensure that the error system is stable and satisfies a prescribed H ∞ norm. Then the existence condition of the reduced-order system matrixes are given and an corresponding iterative linear matrix inequality(LMI) algorithm is presented. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented.

In order to see whether a linear system with ill-conditioned state matrix can be stabilized by static output feedback, by modifying the iterative linear matrix inequality (ILMI) algorithm, a gradient ILMI algorithm is proposed, which used the linear system matrix condition number as the termination term of iteration. Given certain closed loop system robust requirement, the new algorithm can get the maximum degree of stability and give clearly out the feedback gain matrix. Finally, those two algorithms used, the effects are contrasted that the numbers of output feedback variables have on the magnetic levitation control system.

Stability analysis for a class of switched systems with state constraints via time-varying Lyapunov functions

In this paper, the stability and stabilization issue to time-delay affine Takagi-Sugeno (T-S) fuzzy systems is considered. Based on Lyapunov criterion and Razumikhin theorem, an iterative linear matrix inequality (ILMI) algorithm is used to solve the bilinear matrix inequalities (BMI) problem. Besides, ILMI can be used to find the feasible solution for the synthesis of the continuous time-delay affine T-S fuzzy systems. Furthermore, the S-procedure is used in the stability analysis and stabilization procedure in order to provide available analysis results. Finally, a numerical simulation is given to show the applications of the present approach.

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

This paper develops a stability analysis and controller synthesis methodology for a discrete affine fuzzy system based on the convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived. Then, the condition Is recast in the formulation of Linear Matrix Inequalities (LMI) and numerically addressed. The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In synthesis, the stabilizability condition turns out to be in the formulation of nonconvex matrix inequalities and is solved numerically in an iterative manner. Discrete iterative LMI (ILMI) approach is proposed to obtain the feasible solution for the synthesis of the affine fuzzy system. Finally, the applicability of the suggested methodology is demonstrated via some examples and computer simulations.

The paper presents stabilization of a Networked Control System (NCS) with uncertain, time-varying delays using two stabilization approaches namely, Parameter Dependant Lyapunov Function (PDLF) and Quadratic Lyapunov Function (QLF). The PDLF approach depends upon the time varying delay parameters. Thus, for larger delays the system's stability is ensured. In NCS, the uncertainties arising out from the variations in time-delay is modeled using polytopic approach and the stability region of the system is presented in terms of controller gain and maximum tolerable delay. The overall NCS is represented in discrete domain. The proposed PDLF stabilization results have been compared with that of the QLF approach. Lyapunov-based stability criterion is presented in Linear Matrix inequalities (LMIs). The stabilized state feedback controller is designed using LMIs and considering the bounded time-varying delays. The proposed approach is illustrated by two numerical examples. From the results obtained, it is observed that the PDLF approach improves the stability region of the system.

In this paper, sufficient conditions are provided for the stability of switched time-delay systems with polytopic uncertainties. It is assumed that the delay in the system dynamics is time-varying and bounded. Parameter-dependent Lyapunov functionals are employed to obtain exponential stability criteria in the form of linear matrix inequalities (LMI) for the system. Free weighting matrices are then provided to express the relationship between the system variables and the terms in the Leibniz-Newton formula. A numerical example is presented to show the effectiveness of the results obtained.

Local stability analysis of continuous-time Takagi–Sugeno fuzzy systems: A fuzzy Lyapunov function approach

An iterative LMI approach for H∞ synthesis of multivariable PI/PD controllers for stable and unstable processes

The problem of robust constrained model predictive control (MFC) of systems with polytopic uncertainty is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.

In this note, we deal with the stability and stabilization problems for nonlinear quadratic discrete-time periodic systems. By using the quadratic Lyapunov function, and a so called periodic invariant set, delay-independent sufficient conditions for local stability and local stabilization for nonlinear quadratic discrete-time periodic systems are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

This study considers frequency regulation in a hybrid power system consisting of conventional and distributed generation resources. The performance of two controllers—an H ∞ design via linear matrix inequalities and an iterative proportional-integral-derivative H ∞ via linear matrix inequalities—is assessed to maintain frequency deviation profile in acceptable limits. In the latter control design, the iterative linear matrix inequality approach is used to tune proportional-integral-derivative controller parameters subjected to H∞ constraints in terms of the iterative linear matrix inequality. The efficacy of the control law and disturbance accommodation properties is shown. The robustness of these controllers is demonstrated in the hybrid power system with different load disturbance conditions, wind power, and parameter variations. Controller performance is compared with a suboptimal controller to demonstrate its superiority. It is found that the second controller design has satisfactory disturbance rejection properties and robustness against parameter variations over a wide range of conditions.

This paper is concerned with the design of reliable H 221E; fuzzy controller for continuous-time nonlinear systems with time delay and actuator faults. Based on a parameter-dependent Lyapunov Function and general actuator failure (which covers the cases of normal operation, partial degradation and outage), a novel design method of reliable fuzzy controller for T-S Fuzzy system with time varying delay is proposed. The corresponding closed-loop system is asymptotically stable not only when all actuator components are operating well, but also in the presence of some actuator failures. Sufficient conditions are proposed in Linear Matrix Inequality (LMIs) terms by employing different model transformations and techniques. Simulation example shows the effectiveness of the proposed method.

This article addresses the admissibility analysis and state-feedback control synthesis problems of discrete-time polytopic descriptor systems with possibly time-varying parameters. First, we present a new necessary and sufficient strict linear matrix inequality (LMI) condition for the admissibility analysis of linear time-invariant (LTI) descriptor systems. Then, based on the concept of poly-quadratic admissibility, introduced in this article, we extend this result to the admissibility analysis of possibly time-varying parameter-dependent descriptor systems. This extension, which applies to both uncertain and measurable parameters, uses parameter-dependent Lyapunov functions and employs two slack variables. The extended conditions are also expressed as strict LMI conditions which are easily tractable numerically compared to the non-strict ones often encountered when dealing with descriptor systems. Note that we have proposed two separate admissibility analysis conditions: one directly exploitable for state estimation and the other for state-feedback control. The need for different admissibility analysis conditions for each synthesis problem is motivated by the fact that the duality between state estimation and state-feedback control, which hold in the case of measurable parameters, does not hold when dealing with uncertain ones. In our approach, we overcome the absence of such duality by considering a dilation only on the dynamical part of the descriptor system. The application of our analysis result to both robust state-feedback control and polytopic state-feedback control are also presented in this article. Our analysis results extend to descriptor systems, some existing results developed for regular systems.