Singular Large-scale Systems Research Articles

Robust output feedback finite-time stabilization of nonlinear singular large-scale continuous-time systems with delays

Robust output feedback finite-time stabilization of nonlinear singular large-scale continuous-time systems with delays

Criteria for finite-time stability of singular large-scale discrete-time delay systems

This paper concerns a problem of finite-time stability for a class of linear singular large-scale systems with delays. Based on matrix transformations, Lyapunov function method combined with new estimation techniques, we derive sufficient conditions for solving the finite-time stability of the system. A numerical example is given to illustrate the validity and effectiveness of the theoretical results.

Guaranteed cost finite-time control of large-scale singular systems with interconnected delays

The guaranteed cost finite-time control problem of large-scale singular systems subjected to interconnected state delays is addressed in this article. A singular value decomposition approach combining with the Lyapunov function method is proposed to study the problem. Based on the method, delay-dependent sufficient conditions are established to design guaranteed cost controllers, which are presented in terms of tractable linear matrix inequalities. An example with simulation is given to demonstrate the validity and effectiveness of the theoretical results.

New results on robust finite-time stability of singular large-scale complex systems with interconnected delays

In this paper, we provide an efficient approach based on combination of singular value decomposition (SVD) and Lyapunov function methods to finite-time stability of linear singular large-scale complex systems with interconnected delays. By representing the singular large-scale system as a differential-algebraic system and using Lyapunov function technique, we provide new delay-dependent conditions for the system to be regular, impulse-free and robustly finite-time stable. The conditions are presented in the form of a feasibility problem involving linear matrix inequalities (LMIs). Finally, a numerical example is presented to show the validity of the proposed results.

Optimal control of large-scale singular linear systems via hierarchical strategy

This paper states a hierarchical strategy of large-scale singular linear system in which the system is composed of J singular linear subsystems with interconnections. Among hierarchical strategies, the two-level optimization conditions based on Interaction Prediction Method (IPM) are derived such that whole large-scale singular system is optimized. Based on the two-level coordination method, the optimization analysis and controller design of large-scale singular linear system is discussed. For this purpose, two decentralized nonlinear state feedback controllers are designed for each subsystem, such that the whole closed-loop linear system is optimized. These conditions are used to extract two IPM algorithms. Then, by using both algorithms, two numerical examples are given to confirm the analytical results and illustrate the effectiveness of the proposed method.

Finite-time robust decentralized control for uncertain singular large-scale systems with exogenous disturbances

AbstractThis paper considers the problem of finite-time robust decentralized control for uncertain continuous-time singular large-scale systems with exogenous disturbances (UCSLSSED). The concept of finite-time robust decentralized stabilization for UCSLSSED is introduced by definition of finite-time stability for uncertain continuous-time large-scale systems with exogenous disturbances. The analyses of finite-time robust bounded and finite-time robust stabilization for UCSLSSED are done. The design approach of finite-time robust decentralized state feedback controller is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed method.

Decentralised control for complex systems - an invited survey

With the advancement of science and technology, practical systems are becoming more complex. Decentralised control has been recognised as a practical, feasible and powerful tool for application to large scale interconnected systems. In this paper, past and recent results relating to decentralised control of complex large scale interconnected systems are reviewed. Decentralised control based on modern control approaches such as variable structure techniques, adaptive control and backstepping approaches are discussed. It is well known that system structure can be employed to reduce conservatism in the control design and decentralised control for interconnected systems with similar and symmetric structure is explored. Decentralised control of singular large scale systems is also reviewed in this paper.

Stabilization of a Kind of Nonlinear Discrete Singular Large-Scale Control Systems

This paper studies the state feedback stabilization of a kind of nonlinear discrete singular large-scale control systems by using Lyapunov matrix equation, generalized Lyapunov function method and matrix theory. There gives some sufficient conditions for determining the asymptotical stability and instability of the corresponding singular closed-loop large-scale systems while the subsystems are regular, causal and R-controllable. At last, an example is given to show the application of main result. Key words: Nonlinear discrete singular large-scale system; Control system; Asymptotical stability; Stabilization; State feedback

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

State Feedback Stabilization of Discrete Singular Large-scale Control Systems

Abstract: This paper studies the state feedback stabilization of discrete singular large-scale control systems by using Lyapunov matrix equation, generalized Lyapunov function method and matrix theory. There gives some sufficient conditions for determining the asymptotical stability and instability of the corresponding singular closed-loop large-scale systems while the subsystems are regular, causal and R-controllable. At last, an example is given to show the application of main result. Key words: Discrete Singular Large-Scale Control System; Asymptotical Stability; Stabilization; Generalized Lyapunov Function; State Feedback

Decentralized H-infinity state feedback control for discrete-time singular large-scale systems

The decentralized H-infinity control problem for discrete-time singular large-scale systems is considered. Based on the bounded real lemma of discrete-time singular systems, a sufficient condition for the existence of decentralized H-infinity controller for discrete-time singular large-scale systems is presented in terms of the solvability to a certain system of linear matrix inequalities by linear matrix inequality (LMI) approach, and the feasible solutions to the system of LMIs provide a parameterized representation of a set of decentralized H-infinity controller. The given example shows the application of the method.

Robust decentralised stabilisation of interval discrete-time singular large-scale systems

The problem of robust decentralised state-feedback stabilisation for discrete-time singular large-scale systems with interval uncertainties is addressed in this study. By using the matrix norm operation and the rank-1 matrix technique for interval matrices, two sufficient conditions to check the robust decentralised stabilisability of uncertain discrete-time singular large-scale systems are, respectively, obtained. At the expense of problem size (numerical complexity), the second condition gives a less conservative result than the first one. It is therefore reasonable to check the robust stabilisability by the first condition, and then if it fails, resort to the second one. Finally, illustrative examples show that the proposed conditions are effective for the design of robust decentralised stabilising state-feedback controller for not only the uncertain discrete-time singular large-scale systems but also the uncertain discrete-time regular large-scale systems.

Stabilisation of large-scale nonlinear systems by modifying the interconnection network

In this article, we develop a new strategy for the robust stabilisation of large-scale singular systems. The models that we will be concerned with consist of a large number of nonlinear subsystems, which are linked through a linear interconnection network. This approach does not require the availability of control inputs, and focuses instead on variable parameters in the interconnection network. It is shown that the determination of appropriate parameter values reduces to a constrained static output feedback problem, which can be solved using linear matrix inequalities. The proposed method is designed to minimise the number of optimisation variables, and is therefore suitable for large-scale applications. It can also incorporate information structure constraints and uncertainties in the system model.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

Abstract The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality (LMI) via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.

Robust control for discrete-time singular large-scale systems with parameter uncertainty

This paper addresses the problem of robust stabilization for uncertain discrete-time singular large-scale systems with parameter uncertainties. The system under consideration is not necessarily regular. The parameter uncertainties are assumed to be time invariant, but norm-bounded. The purpose of the robust stabilization problem is to design state feedback controllers such that, for all admissible uncertainties, the closed-loop system is regular, causal and stable. In terms of strict LMIs, sufficient conditions for the solvability of the problem is presented, and the parameterization of desired state feedback controllers is also given. A numerical example is given to demonstrate the applicability of the proposed design approach.

Decentralized Adaptive Control for Large-Scale Singular Systems with Series Nonlinearities

This paper concerns with the decentralized adaptive variable structure control for a class of perturbed large-scale singular systems with series input nonlinearities. Based on the Lyapunov stability theorem, a decentralized adaptive variable structure controller is developed. The limitation of knowing the upper bounds of the uncertainties is released due to the adaptive scheme in this paper. The proposed controller ensures the occurrence of the sliding manifold of the composite singular system even subjected to input nonlinearity. It shows that the uncertain nonlinear singular large-scale system also possesses the property of insensitivity to uncertainties and disturbances as a linear system does.

Stability of singular large-scale systems in the presence of structural perturbations

We investigate the problem of the stability of singularly perturbed LSS with structural perturbations in the case of a nonuniformly graduated time scale. We employ Lyapunov's method based on a matrix valued function

Uniform asymptotic stability of singular large-scale systems subjected to structural perturbations

Uniform asymptotic stability of singular large-scale systems subjected to structural perturbations