Negative-Definite Domain Approach for Nonlinear Dynamic Output Feedback Stabilization with DOA Estimation

The paper mainly deals with the problem of finite-time stabilization of linear time-varying systems. A dynamic output feedback controller is designed, which is able to stabilize the linear time-varying systems in finite time. By virtue of extended piecewise constant method, novel criteria for the existence of a dynamic output feedback controller is established in terms of linear matrix inequalities. Compared with the existing method, the proposed method is more efficient from a computational point of view. A simulation is given to illustrate the effectiveness of the obtained result.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

This paper considers the problem of adaptive reliable guaranteed cost controller design for linear time-delay systems against actuator faults via dynamic output feedback. Based on indirect adaptive method, a new reliable dynamic output feedback controller is established. The controller gains are affinely dependent on the estimations of fault parameters, which are updating automatically according to the proposed adaptive laws. New delay-dependent sufficient conditions for the existence of the reliable guaranteed cost dynamic output feedback controller are derived in terms of linear matrix inequalities, which have less conservativeness than the corresponding reliable dynamic output feedback controller with fixed gains. An example is presented to show the effectiveness of the proposed method.

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

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In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.

This paper addresses the dynamic output feedback stabilization problem for linear time-invariant systems where the process disturbance preview is available to the controller via communication networks. A lower bound of data rates of communication channels, above which there exists a feedback control policy to stabilize the unstable plant with unbounded disturbance, is presented. Furthermore, the problem of bandwidth allocation in the communication channel is analyzed based on the system dynamics. Simulation results show the validity of the proposed scheme.

This paper investigates the dynamic output feedback control for a class of nonlinear time-delay system with the triangular structure-type uncertain nonlinearity satisfying the linear growth condition. A dynamic observer-based output feedback robust stabilizing controller is presented on the basis of Lyapunov-Razumikhin function design strategy. A numerical example is given to illustrate the effectiveness of this method.

This paper considers the design problem of dynamic output feedback control for fractional-order (FO) Takagi-Sugeno fuzzy systems with uncertain parameters. Via the application of FO system stability theory, robust control method and the linear matrix inequality techniques, sufficient conditions are given for the stability analysis and the existence of the dynamic fuzzy output feedback controllers. The dynamic output feedback controller designed here guarantees the robust stability of the closed-loop system. Finally, a fractional order chaotic system simulation example is given to illustrate the effectiveness of the design approach here.

In terminal guidance phase, only partial information concerning the interception geometry is available. To intercept a target in specified direction under this condition, an impact angle constrained guidance law is proposed based on the dynamic output feedback. The guidance law doesn't use the rate of line-of-sight angle, and can guarantee convergence speed of the closed-loop system. Utilizing the parametric algebraic Riccati equation, a dynamic output feedback controller is designed. The controller contains a feedback law and an observer is obtained. Through integrated design of the parameters of the feedback law and the observer, the closed-loop system can be transformed to a new system, whose system matrix is a Jordan matrix. Using Lyapunov approach, desired convergence speed of the new system can be obtained by tuning its poles. And the same convergence speed of the original closed-loop system can also be achieved. Based on the dynamic output feedback controller, an impact angle constrained guidance law is derived. The guidance law is demonstrated by numerical simulation. Convergence speed can be guaranteed by the guidance law, and high guidance precision is achieved.

The H∞ dynamic output feedback control problem for a class of discrete‐time switched time‐delay systems under asynchronous switching is investigated in this paper. Sensor nonlinearity and missing measurements are considered when collecting output knowledge of the system. Firstly, when there exists asynchronous switching between the switching modes and the candidate controllers, new results on the regional stability and l2 gain analysis for the underlying system are given by allowing the Lyapunov‐like function (LLF) to increase with a random probability. Then, a mean square stabilizing output feedback controller and a switching law subject to average dwell time (ADT) are obtained with a given disturbance attenuation level. Moreover, the mean square domain of attraction could be estimated by a convex combination of a set of ellipsoids, the number of which depends on the number of switching modes. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

In this work, we develop a method for dynamic output feedback covariance control of the state covariance of linear dissipative stochastic partial differential equations (PDEs) using spatially distributed control actuation and sensing with noise. Such stochastic PDEs arise naturally in the modeling of surface height profile evolution in thin film growth and sputtering processes. We begin with the formulation of the stochastic PDE into a system of infinite stochastic ordinary differential equations (ODEs) by using modal decomposition. A finite-dimensional approximation is then obtained to capture the dominant mode contribution to the surface roughness profile (i.e., the covariance of the surface height profile). Subsequently, a state feedback controller and a Kalman-Bucy filter are designed on the basis of the finite-dimensional approximation. The dynamic output feedback covariance controller is subsequently obtained by combining the state feedback controller and the state estimator. The steady-state expected surface covariance under the dynamic output feedback controller is then estimated on the basis of the closed-loop finite-dimensional system. An analysis is performed to obtain a theoretical estimate of the expected surface covariance of the closed-loop infinite-dimensional system. Applications of the linear dynamic output feedback controller to the linearized stochastic Kuramoto-Sivashinsky equation are presented.

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

Dynamic Output Feedback Stabilization of Non-uniformly Observable Dissipative Systems

The aim of the paper is the output feedback stabilization of a class of single-input single-output (SISO) nonlinear systems. We deal with a class of systems, so-called triangular form systems, that may have unobservable and unstabilizable approximate linearization about the origin. This kind of systems, referred to as singular triangular forms, may neither be stabilized by a smooth state feedback nor smoothly detectable. However, under certain simple conditions, it is known to be stabilizable by a static state feedback. A solution to continuous dynamic output feedback stabilization is proposed. This is based on the construction of the continuous observer and nonlinear analogue of the well known separation principle. The resulting observer may be computed and tuned in a straightforward constructive way. Numerical simulation of selected examples are performed to underline the applicability of the presented approach and to illustrate good convergence of both observer and controller system.