Dynamic Output Feedback Stabilization Research Articles

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

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

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Stabilizing Design of Third-Order Continuous-Time Switched Linear Systems

In this work, we address both the state feedback stabilization problem and the dynamic output feedback stabilization problem for third-order continuous-time switched linear systems. Based on the controllability normal form decomposition approach, we prove that any controllable system is state feedback stabilizable, and the rate of convergence could be arbitrarily pre-assigned. Furthermore, for observable switched systems, we propose a reduced-order observer that could asymptotically estimate the unmeasured states. The dynamic output feedback stabilization problem is solved by designing a common switching law that stabilizes both the state and the observer. The design process is completely constructive.

Robust H∞$H_\infty$ dynamic output feedback control of the DC–AC converter with a neutral leg

This paper investigates the problem of robust H ∞ $H_\infty$ dynamic output feedback control of 3-phase 4-wire converter with neutral bridge arm in the application of smart grid and distributed generation. Based on Lyapunov functions, a novel sufficient Linear Matrix Inequality condition analysis was performed on the dynamic output feedback stabilisation controllers. Meanwhile, some auxiliary slack variables with special structure and well-established performance conditions are employed to reduce design conservatism. This topology along with the H ∞ $H_\infty$ controller can solve the DC link balancing problem and maintain the deviation between the neutral point and the midpoint of DC supply very small. The achievable performance is analysed quantitatively and the controller design method was conducted and verified both in MATLAB simulation and the real-time simulation platform built by StarSim and MT, respectively.

Robust dynamic output feedback stabilization for uncertain singular Markovian jump systems with time‐varying delays

AbstractThe article investigates robust dynamic output feedback (DOF) stabilization for uncertain time‐varying delays singular Markovian jump systems (SMJSs). First, by using improved Lyapunov–Krasovskii functional, sufficient conditions of robust admissibility (namely regularity, non‐impulsiveness, and asymptotic stability) for unforced nominal time‐varying delays SMJSs are given. Second, by constructing a DOF controller such that the resulting closed‐loop system satisfies robust admissibility, the robust DOF stabilization problem is solved in terms of linear matrix inequalities via orthogonal complement technique. Finally, the availability and practicality of the prime results are certified by two numerical examples and a practical example of the oil catalytic cracking process.

Global dynamic output feedback stabilization for a class of high‐order nonlinear systems

AbstractThis article discusses the issue of global dynamic output feedback stabilization for a class of high‐order nonlinear systems. At first, an output feedback controller (OFC) is designed for the nominal system by virtue of adding one power integrator technique. Then, two dynamic gains are introduced into the proposed OFC to implement global stabilization of the closed‐loop system. Moreover, the proposed method can be broadened to a family of high‐order upper‐triangular nonlinear systems. To the end, two examples are given to illustrate the effectiveness of the proposed method.

Dynamic output feedback stabilization of deterministic finite automata via the semi-tensor product of matrices approach

This paper deals with the dynamic output feedback stabilization problem of deterministic finite automata (DFA). The static form of this problem is defined and solved in previous studies via a set of equivalent conditions. In this paper, the dynamic output feedback (DOF) stabilization of DFAs is defined in which the controller is supposed to be another DFA. The DFA controller will be designed to stabilize the equilibrium point of the main DFA through a set of proposed equivalent conditions. It has been proven that the design problem of DOF stabilization is more feasible than the static output feedback (SOF) stabilization. Three simulation examples are provided to illustrate the results of this paper in more details. The first example considers an instance DFA and develops SOF and DOF controllers for it. The example explains the concepts of the DOF controller and how it will be implemented in the closed-loop DFA. In the second example, a special DFA is provided in which the DOF stabilization is feasible, whereas the SOF stabilization is not. The final example compares the feasibility performance of the SOF and DOF stabilizations through applying them to one hundred random-generated DFAs. The results reveal the superiority of the DOF stabilization.

Robust ℋ∞ and ℒ∞–ℒ∞ sampled-data dynamic output-feedback control for nonlinear system in T–S form including singular perturbation

ABSTRACT This paper pays attention to the robust sampled-data dynamic output-feedback stabilisation problems for a singularly perturbed nonlinear system in Takagi–Sugeno (T–S) form when the system suffers from parametric uncertainties and or disturbances. Two design conditions are proposed in terms of linear matrix inequalities such that the admissible controllers guarantee the prescribed and – disturbance-attenuation levels, respectively. The features of the development are that (i) the sampled-data syntheses are performed in a continuous-time domain and (ii) (even approximate) discrete-time modelling of the T–S fuzzy system is not involved.

New perspectives on output feedback stabilization at an unobservable target

We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. We illustrate two main ideas: well chosen perturbations of a state feedback law can yield new observability properties of the closed-loop system, and embedding systems into bilinear systems admitting observers with dissipative error systems allows to mitigate the observability issues. We apply them on a case of systems with linear dynamics and nonlinear observation map and make use of an ad hoc finite-dimensional embedding. More generally, we introduce a new strategy based on infinite-dimensional unitary embeddings. To do so, we extend the usual definition of dynamic output feedback stabilization in order to allow infinite-dimensional observers fed by the output. We show how this technique, based on representation theory, may be applied to achieve output feedback stabilization at an unobservable target.

Dynamic Output Feedback Stabilization of Non-uniformly Observable Dissipative Systems

Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback stabilization. In this paper, we present a methodology to overcome this challenge in the case of dissipative systems by requiring only target detectability. These systems appear in many physical systems and we provide various examples and applications of the result.

Output-feedback stabilization for descriptor Markovian jump systems with generally uncertain transition rates

Abstract This paper presents a dynamic output-feedback stabilization problem of descriptor Markovian jump systems with generally uncertain transition rates. First, a new necessary and sufficient condition to relax inequalities including generally uncertain transition rates is introduced. For the closed-loop systems with a dynamic output-feedback controller, the stabilization criterion is achieved as non-convex matrix inequalities. For the obtained criterion, this paper gives an improved necessary and sufficient condition in terms of linear matrix inequalities under completely known transition rates. Then, the proposed condition is extended for the descriptor Markovian jump systems with generally uncertain transition rates. To show the validity of the proposed control, a numerical example is given.

Necessary and sufficient conditions for the dynamic output feedback stabilization of fractional-order systems with order 0 < α < 1

Necessary and sufficient conditions for the dynamic output feedback stabilization of fractional-order systems with order 0 < α < 1

Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with partly unknown transition rates. First of all, for the augmented systems, the stabilization conditions are formulated in terms of non-convex matrix inequalities. For these conditions, this paper successfully derives new necessary and sufficient conditions in the form of linear matrix inequalities under partly unknown transition rates by using the variable elimination technique. Two numerical examples are provided to demonstrate the validity of the derived results.

Output-feedback control for singular Markovian jump systems with input saturation

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with input saturation. The stabilization and set invariance conditions are first formulated in terms of non-convex matrix inequalities which is not linear matrix inequalities (LMIs). This paper, however, successfully derives the necessary and sufficient conditions for the non-convex inequalities in terms of LMIs. Also, an optimization problem is formulated to find the largest contractively invariant set in mean square sense of the closed-loop systems. Two numerical examples show the validity of the derived results.

Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach

A new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable.

Finite-time dynamic output feedback stabilization of linear time-varying systems by a piecewise constant method

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.

Control of Nonlinear Systems Subject to Amplitude Bounded Disturbances Using a N-fuzzy Strategy

Abstract The dynamic output feedback stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) N-fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a dynamic output feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Furthermore, the proposed approach enables to handle with nonlinearities that are not function of the measured outputs but are sector bounded. A numerical example is considered to illustrate the effectiveness of the developed technique.

Dynamic Output-Feedback Control for Singular Markovian Jump System: LMI Approach

For the dynamic output-feedback stabilization of continuous-time singular Markovian jump systems, this paper introduces the necessary and sufficient condition , whereas the previous research works suggested the sufficient conditions. A special choice of the block entries of Lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities . A numerical example shows the validity of the derived results.

Dynamic output‐feedback stabilisation for Markovian jump systems with incomplete transition description and input quantisation: linear matrix inequality approach

In this study, a dynamic output-feedback stabilisation problem for Markovian jump systems (MJSs) with incomplete transition description and input quantisation is investigated. While the previous researches about output-feedback stabilisation for MJSs assumed that the transition rates are completely known, a more general situation where the transition rates are partly unknown is considered. Moreover, the proposed controller includes non-linear control part to eliminate the effect of input quantisation. Two numerical examples are provided to demonstrate the feasibility of the proposed dynamic output-feedback controller.

The output feedback control synthesis for a class of singular fractional order systems

This paper investigates the output feedback normalization and stabilization for singular fractional order systems with the fractional commensurate order α belonging to (0,2). Firstly, an effective criterion for the normalization of singular fractional order systems is given with output differential feedback. Afterwards, both static and dynamic output feedback stabilization of such normalized fractional order systems are derived. Besides, the robustness to the parameter uncertainty and the initial conditions are discussed in detail. All the results are given via linear matrix inequality (LMI) formulation. Finally, three numerical examples are provided to demonstrate the applicability of the proposed approaches.