Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions

Establishing robust stability of discrete-time systems with time-varying uncertainty: The Gram-SOS approach

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

The robust stability of linear continuous-time uncertain systems in polytopic domains is investigated in this paper. The uncertain parameters are assumed as time-varying with bounded rates of variation. The robust stability conditions are obtained from the definition of a Lyapunov function with a particular structure, depending on integer powers κ of the dynamic uncertain matrix of the system. As a consequence, parametrized linear matrix inequalities conditions are obtained in terms of κ. As κ grows, the robust stability conditions can take into account bounds on the successive time-derivatives of the uncertain parameters, reducing the conservativeness of the evaluations. Numerical examples illustrate the effectiveness of the proposed methodology.

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

Deals with the problem of robust stability of linear systems with uncertain real time-varying parameters with magnitudes and rates of change (or variations, in discrete-time) which are confined to a given convex region. A notion of robust stability, referred to as bi-quadratic stability, which is based on a Lyapunov function that depends quadratically on the uncertain parameters is proposed. LMI based sufficient conditions for bi-quadratic stability of continuous- and discrete-time systems are developed. The proposed stability analysis methods have the advantage that they can be used for solving problems of robust control synthesis, including robust stabilization, robust H/sub 2/ control, and robust H/sub /spl infin// control.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

The Lyapunov function method is used to study the robust absolute stability of general interval Lurie control systems, and algebraic sufficient conditions are obtained for the general interval Lurie type control systems. A relationship between the stability of the symmetric interval matrix and robust absolute stability of general interval Lurie type control systems is established.

This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-/spl mu/ analysis, and numerical experiments indicate that they often compare favorably with /spl mu/ analysis for time-invariant parameter uncertainty.

Delay-dependent robust stability analysis and stabilization of linear systems using a simple delay-discretization approach

This paper investigates the problem of the robust delay-dependent stability for uncertain stochastic systems with interval time-varying delays. By establishing a new Lyapunov function and using the convex function theory, the delay-dependent sufficient criteria is derived in terms of linear matrix inequalities (LMIs), which takes into account the range of the upper and lower bound of interval time-varying delays. A numerical example is given to illustrate the effectiveness of the proposed method.

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is respectively obtained for the stability and stabilizability of the considered system. Moreover, an example with simulations is given to verify the effectiveness of our theoretical results.

This article presents a new approach to robust quadratic stabilization of nonlinear stochastic systems. The linear rate vector of a stochastic system is perturbed by a nonlinear function, and this nonlinear function satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of stochastic systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The new formulation provides a suitable setting for robust stabilization of nonlinear stochastic systems where the underlying deterministic systems satisfy the generalized matching conditions. Our sufficient conditions are written in matrix forms, which are determined by solving linear matrix inequalities (LMIs), which have significant computational advantage over any other existing techniques. Examples are given to demonstrate the results.

The robust stability analysis for discrete large-scale uncertain systems with multiple time delays is addressed in this paper. We establish a method for selecting properly a positive definite matrix Q to derive a very simple upper solution bound of the discrete algebraic Lyapunov equation (DALE). Then, using the Lyapunov equation approach method with this upper bound, several sufficient conditions are presented to guarantee the robust stability of the overall systems. Comparisons between the proposed results with a previous one are also given.

On Absolute Stability of Lur’e Control Systems with Multiple Non-Linearities

The authors consider the class of nonnegative discrete-time systems and analyze the matrix theoretical results involving nonnegative maintainability with respect to the problem of robust stabilization of interval discrete systems. Using state feedback, a controller which may include an observer such that the closed-loop interval system is robustly stabilized and at the same time becomes nonnegative is designed. The procedure is to characterize the set of robust controllers by means of matrix inequalities, and to choose a suitable controller by solving an optimization algorithm. >