Robust dichotomy and controller design for a class of nonlinear systems

This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities (LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua's circuit shows the applicability of the proposed approach.

In this paper, we investigate the problem of robust H ∞ control for singular systems with polytopic time-varying parameter uncertainties. By introducing the notion of generalized quadratic H ∞ performance, the relationship between the existence of a robust H ∞ dynamic state feedback controller and that of a robust H ∞ static state feedback controller is given. By using matrix inequalities, the existence conditions of robust H ∞ static state feedback and dynamic output feedback controllers are derived. Moreover, the design methods for such controllers are provided in terms of the solutions of matrix inequalities. An example is also presented to demonstrate the validity of the proposed methods.

To avoid the bumps of the control signal in the switching instants, this paper proposes a bumpless transfer control method which guarantees the continuous of control signal while keeping the asymptotic stability of the closed-loop system. Firstly, the presented bumpless transfer control method possesses a simple structure and meanwhile not have to redesign sub-controllers, which is easy to implement. Furthermore, the method is appropriate for either stable subsystems or unstable subsystems, and be suitable for either state feedback control or dynamic output feedback control. Moreover, we give the sufficient conditions of asymptotic stability for switched linear systems under bumpless transfer control for four cases. For the original switched system with stable subsystems under state or dynamic output feedback control, the stability conditions under mode-dependent average dwell time switching are derived. For the original switched system with unstable subsystems under state or dynamic output feedback control, which is stabilized by some certain switching laws, the stability conditions under the original switching law are given. Finally, a hardware-in-the-loop simulation of an aero-engine control system is employed to verify the effectiveness and superiority of the proposed method.

This paper presents a comprehensive investigation on the $${{\mathcal H}_{\infty}}$$ control problem of linear multidimensional (nD) discrete systems described by the nD Roesser (local) state-space model. A Bounded Real Lemma consisting of a series of conditions is first established for general nD systems. The proposed nD conditions directly reduce to their 1D counterparts when n = 1, and besides several sufficient conditions which include the existing 2D results as special cases, some necessary and sufficient conditions are also shown to explore further insights to the considered problem. By applying a linear matrix inequality (LMI) condition of the nD Bounded Real Lemma, the nD $${{\mathcal H}_{\infty}}$$ control problem is then considered for three kinds of control laws, namely, static state feedback (SSF) control, dynamic output feedback (DOF) control and static output feedback (SOF) control, respectively. The nD $${{\mathcal H}_{\infty}}$$ SSF and DOF control problems are formulated in terms of an LMI and LMIs, respectively, and thus tractable by using any available LMI solvers. In contrast, the solution condition of the nD $${{\mathcal H}_{\infty}}$$ SOF controller is not strictly in terms of LMIs, therefore an iterative algorithm is proposed to solve this nonconvex problem. Finally, numerical examples are presented to demonstrate the application of these different kinds of nD $${{\mathcal H}_{\infty}}$$ control solutions to practical nD processes as well as the effectiveness of the proposed methods.

This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty. We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness. Both linear static state feedback and dynamic output feedback controllers are considered. First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established. Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach. As for uncertain systems, we consider structured uncertainty characterized by a dissipative system. This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. LMIbased methods for designing robust dissipative controllers are also derived. The results of this paper unify existing results on H and positive real control and provide a more flexible and less conservative robust control design as it allows for a better trade-off between phase and gain performances.

Robust [formula omitted] control of uncertain differential linear repetitive processes

The design of state feedback controllers and dynamic output feedback controllers is given for a class of Lipschitz nonlinear systems. We transform the nonlinear systems into linear parameater varying (LPV) systems by the use of the differential mean value theorem (DMVT). A sufficient condition is provided by using linear matrix inequalities (LMIs) and the state feedback controllers and dynamic output feedback controllers are gained. When the feedback control laws are applied to the systems, the closed-loop systems are globally asymptotically stable. A simulation example shows the feasibility and effectiveness of the conclusion.

SUMMARYThis paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.

This work concerns the problem of feedback design for pendulum-like systems guaranteeing gradient-like behavior. The uncertain system under consideration is described by a state-space model, which contains parameter uncertainties in both the state and input matrices. The nonlinearity is assumed to be periodic and slope restricted. First, the frequency-domain inequalities condition of gradient-like behavior is converted into a linear matrix inequalities (LMI) based criterion. Then the result is extended to take into account the parameter norm-bounded uncertainties in the linear part and derive static state feedback controller and dynamic output feedback controller such that the resulting closed-loop system is gradient-like. Schemes of designing controller as well as parameterized form of controllers are presented. Illustrative example is given to show the effectiveness of the proposed approach.

This paper discusses the problems of the finite-time annular domain stability (FTAD-stability) and stabilization of discrete-time stochastic systems (DTSS). First, a definition of FTAD-stability for DTSS is given and a stability criterion is also proposed. Second, we respectively give some sufficient conditions for the existence of state feedback controller (SFC), static output feedback controller (SOFC) and dynamic output feedback controller (DOFC). Finally, a numerical example is utilized to show the effectiveness of proposed method.

This paper considers globally asymptotic stabilization for a class of singular bilinear systems. By the system matrices a sufficient condition for the globally asymptotic stabilization is presented and under the condition continuous static state feedback and dynamic output feedback controllers are constructed, respectively. By means of LaSalle invariant principle and the separation principle for singular nonlinear systems the globally asymptotic stability of the closed loop systems is verified.

The finite time horizon H ∞-control problems for nonlinear time-varying systems are considered where the initial state is unknown. They are solved by using both static state feedback and dynamic output feedback controllers. A class of nonlinear H ∞-controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters. The solvability for nonlinear finite time horizon H ∞-control problem requires suitable solutions to some Hamilton-Jacobi inequalities (equations).

Presents a method of controlling the first three vibration modes of a flexible structure using H-infinity optimal control. A feedback controller is designed based on the reduced order model and is capable of attenuating vibration without causing spillover instability. For this purpose, a three degree of freedom lumped parameter mass model of a plate structure is considered to control its vibrations using a dynamic output feedback controller and a static state feedback controller. The actuator dynamics and the placement of actuators are considered for an effective controller design method. The efficacy of both type of controllers is verified through experimental studies and compared.

This article considers the problem of designing a static feedback control for a linear time invariant system such that a specified set of expensive sensors, used for state measurements, are eliminated. If a particular column of the feedback gain matrix is entirely zero, then the state corresponding to that column is not required to be measured, and hence, the corresponding sensor can be eliminated. With this observation, a structured feedback gain matrix is designed where the columns, corresponding to the specified expensive sensors, are made entirely zero. The desired transient behaviour is achieved by assigning the poles of closed loop system in a suitably chosen region in the left half of the complex plane. A linear matrix inequality (LMI) feasibility problem is formulated to compute the desired gain matrix. The developed methodology is demonstrated with practical examples.

ABSTRACTThis paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.