Stability Of Linear Descriptor Systems Research Articles

Addressing stability challenges in linear descriptor systems: A unified approach to robust control

This paper focuses on studying the robust stability of linear descriptor systems with perturbations in the state matrix under rank-deficient and unmatched conditions. In fact, there are three main steps in this study. The first is constructing an equivalent optimal control to design a robust control. The second step is to solve the Riccati equation to find the optimal control solution. The third step is to implement the cost function of the equivalent optimal control to define the candidate Lyapunov function in order to verify the stability conditions. The proposed control method is verified through simulations. Our results demonstrate that the proposed approach can guarantee robust stability under uncertain and perturbed conditions.

State feedback stabilization of linear descriptor time-varying delay systems

In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

Robust Stabilization and Weighted Damping of Bounded Disturbances in Descriptor Control Systems

We establish necessary and sufficient conditions for the existence of dynamic regulators guaranteeing the prescribed estimation of the weighted level of damping of bounded disturbances and the asymptotic stability of linear descriptor systems. An algorithm for the construction of these regulators in the problems of robust stabilization and generalized H∞-optimization is proposed for the descriptor systems with controlled and observed outputs. The main computational procedures of the algorithm are reduced to the solution of linear matrix inequalities with additional rank restrictions. The efficiency of the algorithm is demonstrated by an illustrative example of descriptor stabilization system with bounded disturbances.

Stability Analysis of Linear Polytopic Descriptor Systems Using a Novel Copositive Matrix Approach

In this paper, we propose a copositive matrix approach to study stability of linear descriptor systems with polytopic uncertainty. First, by using copositive matrix analysis, new stability conditions are established in terms of linear matrix inequalities ensuring the regularity, impulse free, and exponential stability of such systems. Then, we use the obtained results to provide stability conditions for the system with delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Robust State‐Derivative Feedback LMI‐Based Designs for Linear Descriptor Systems

Techniques for stabilization of linear descriptor systems by state‐derivative feedback are proposed. The methods are based on Linear Matrix Inequalities (LMIs) and assume that the plant is a controllable system with poles different from zero. They can include design constraints such as: decay rate, bounds on output peak and bounds on the state‐derivative feedback matrix K, and can be applied in a class of uncertain systems subject to structural failures. These designs consider a broader class of plants than the related results available in the literature. The LMI can be efficiently solved using convex programming techniques. Numerical examples illustrate the efficiency of the proposed methods.

A complex projection scheme and applications

In this paper, an extended projection method in the complex number field is presented. We consider two classes of complex linear matrix inequalities and then derive the corresponding projection operators. Applications to the control system with pole assignment problem and the robust stability of linear descriptor systems, which are described in complex linear matrix inequalities, are given. Based on the numerical algorithms, some examples are illustrated for the merits of the proposed method.

On the stability of linear descriptor systems by applying modified Lyapunov equations

On the stability of linear descriptor systems by applying modified Lyapunov equations

Stability of linear descriptor systems with delay: a Lyapunov-based approach

The Lyapunov second method is developed for linear coupled systems of delay differential and functional equations. By conventional approaches such equations may be reduced to the neutral systems and the known results for the latter may be exploited. In the present paper we introduce a new approach by constructing a Lyapunov–Krasovskii functional that corresponds directly to the descriptor form of the system. Moreover, by representing a neutral system in the descriptor form we obtain new stability criteria for neutral systems which are less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability and for robustness of stability with respect to small delays are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.

線形ディスクリプタシステムの二次安定性と二次安定化

線形ディスクリプタシステムの二次安定性と二次安定化

ディスクリプタシステムに対する等式制約を含まないLMI安定条件とそのロバスト安定化への応用

ディスクリプタシステムに対する等式制約を含まないLMI安定条件とそのロバスト安定化への応用

Quadratic stabilization of Linear Descriptor systems

This paper presents necessary and sufficient conditions for a linear descriptor system to be quadratically stabilizable via linear feedback control. Uncertainties in the system are structured and norm-bounded. It is assumed that the system has no impulsive mode and the coefficient matrix for the derivative of the descriptor variable has no uncertainty. Quadratic stabilizability is defined by introducing a positive semidefinite quadratic function which is, however, positive definite for dynamic behaviors of the descriptor variable. The stabilizability conditions are described in terms of the existence of certain solutions of a generalized algebraic Riccati equation.

Consistency and Liapunov Stability of Linear Descriptor Systems: A Geometric Analysis

Consistency and Liapunov Stability of Linear Descriptor Systems: A Geometric Analysis