Robust PD State Feedback Controller Design for Uncertain Singular Systems

In this paper, we consider the problems of robust stability and stabilization of Lurpsilae control systems with time-varying delay. Firstly, by making use of an integral inequality, some delay-dependent robust stability conditions of the system are presented. Then, a sufficient stabilization criterion is established in the terms of linear matrix inequality (LMI), based on the above stability condition and matrix decomposition technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

This paper discusses strict linear matrix inequalities(LMIs) sufficient condition which can be removed of the equality constraint for linear continuous singular systems. The criteria of stability and stabilization of continuous singular system are presented. The conditions are expressed in terms of strict positive definite LMIs which can reduce the equality constraint and semi-positive definite LMIs and are much more tractable and reliable in numerical computation than existing conditions. The conditions make use of only the system parameter matrices (E, A, B) directly by a restricted equivalent transform without introducing other adjective parameters. A counterexample is given to illustrate the criteria are only a sufficient condition but not are a necessary condition. The idea presented can help to find necessary and sufficient strict LMI criteria without equality constraint conditions of stability and stabilization of continuous singular system.

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse‐free). Based on this, the state‐feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.

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.

The problem of robust stability and stabilization of stochastic large-scale delay systems has been investigated in recent years. However, the robust exponential stability and stabilization has not been considered. The purpose of this paper is to present delay-dependent criteria for robust decentralized exponential stabilization of the complex systems. The obtained results are based on algebraic Riccati equations and may be extended by using the widely-used LMI techniques.

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H/sup infinity / optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H/sup infinity / control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H/sup infinity / control theory-based methods. >

In previous works the authors proposed to use hit-and-run versions of Markov-chain Monte-Carlo algorithms for various problems of control and optimization. In this paper we focus on robust stabilization applications of the method. The crucial notion for this algorithm is a boundary oracle (BO), and we start with constructing BO for robustness problems, including robust stability of polynomials and robust LMIs. Numerical results for various control applications are presented. In particular, we consider a problem arising in control of helicopters. Simulations confirm that the randomized approach can be an effective tool for solving robust stability and robust stabilization problems.

In this note, the problem of delay-dependent robust stabilization for singular systems with multiple time-varying state delays has been investigated, and the problem is solved via state feedback controller in terms of a linear matrix inequality technique. Numerical examples are given to show the validity of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

In this paper,the problem of robust stability and stabilization for a class of singular jumping systems is considered.In the system,the parametric and the transition rate's uncertainties are assumed to be norm bounded.By constructing a stochastic Lyapunov-Krasovskii functional,sufficient conditions are provided such that the system is regular,impulse-free and stochastically stable in mean square sense for all admissible uncertainties.Finally,a numerical example is given to demonstrate the effectiveness of the proposed methods.

This paper focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. First, a convex hull representation is used to describe the saturation characteristics. By constructing an appropriate copositive type Lyapunov functional, we give sufficient conditions for the existence of a state feedback controller such that the closed-loop system is positive and asymptotically stable at the origin of the state space with a domain of attraction. Then, the disturbance rejection performance analysis in the presence of actuator saturation is developed viaL1-gain. The design method is also extended to investigate the problem ofL1-gain analysis for uncertain positive systems with time-varying delays and actuator saturation. Finally, three examples are provided to demonstrate the effectiveness of the proposed method.

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

This paper considers the problem associated with the stability analysis and stabilization for singular systems with multiple time-varying delays. The delay-dependent stability criterion and the method of designing state feedback stabilization controller are obtained by using Lyapunov second method and LMI techniques. Numerical examples illustrate the efficiency and feasibility of our method.