Robust Output Feedback Design of Linear Discrete-Time Systems - LMI Approach

This paper investigates the problem of robust output feedback stabilization of uncertain Hamiltonian systems with saturating actuator and input delay. The uncertainties are assumed to be time invariant and belong to convex bounded polytopic domain. By employing Lyapunov-Krasovskii functional method and Wirtinger's inequality, some sufficient conditions are derived for stabilization of nonlinear Hamiltonian systems under consideration. A delay-independent condition in terms of linear matrix inequalities for control of the Hamiltonian systems is established first. And further, an output feedback controller synthesis scheme under the multiple Lyapunov functional framework is proposed which guarantees the robust stability of the closed-loop system when control saturation and delay effectively occur. Finally, numerical results are given to demonstrate the effectiveness of the proposed methodology.

In this paper, the problem of delay-dependent robust dynamic output feedback stabilization for a class of uncertain singular time-delay system is investigated. Based on the delay-dependent stability criterion for nominal singular time-delay systems and the concept of generalized quadratic stabilization, the sufficient conditions of the existence of the feedback controller are obtained, which ensure that the closed-loop systems are regular, impulse free and robustly asymptotically stable. Moreover, the expression for the desired robustly stabilizing controller is given by using the LMIs and the cone complementarity linearization iterative algorithm.

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.

Describes a direct way to solve the robust output feedback stabilization problem for a class of uncertain nonlinear systems with nonlinear parameterization using the backstepping technique. The backstepping method is performed in a batch way rather than recursively. The paper begins with the stabilization of a system containing a series of integrators with unknown gains. The solution of the problem is then used to solve the output feedback stabilization problem of the nonlinear system.

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.

By using the stochastic optimization approach of Luus and Jaakola [1], a large class of stabilization problems can be readily solved. Application of the approach to the output feedback stabilization problem and the multivariable stability example of Anderson et al. [2] is discussed and illustrated.

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.

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.

This paper considers the problem of stability and robust stabilization for a class of uncertain time delay switched systems using the delta operator. Based on multiple Lyapunov-Krasovskii function in delta domain, a sufficient condition for the existence of stability of the delta operator time delay switched system is presented, and a new sampling period and delay dependent design approach to robust state feedback controller is addressed. The proposed controller can robustly stabilize the uncertain delta operator time delay switched system for all admissible parameter perturbations. The solution to the controller is formulated in the form of a set of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of the developed method.

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 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.

This paper is concerned with the problem of robust stability and stabilization of singular systems with uncertainties in both the derivative and state matrices. By using a parameter dependent Lyapunov function, we derive the LMI-based sufficient conditions for the stabilization of the singular systems. Secondly, by solving these LMIs, a proportional plus derivative (PD) state feedback controller is designed for the closed-loop systems to be quadratically normal and quadratically stable (QNQS). Finally, the numerical example is given to show the effectiveness of the proposed theorems.

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.

The robust output feedback stabilization problem for state-delayed systems with time-varying delays and saturating actuators is addressed here. The systems considered are continuous-time, with parametric uncertainties entering all the matrices in the system representation. A saturating control law is designed and a region of initial conditions is specified within which local asymptotic stability of the closed-loop system is ensured. The least conservative approach that employs the Lyapunov–Krasovskii functional is adopted to ensure stabilization. The designed controller is dependent on the time-delay and its rate of change. The controller is constructed in terms of the solution to a set of matrix inequalities.

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.