Robust output feedback stabilization via a small gain theorem

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.

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.

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.

Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation

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.

This paper studies the class of uncertain dynamical time-delay linear systems with Markovian jumps. The time-delay is assumed to be dependent on the system mode. LMI-based sufficient conditions for the robust stability and output feedback stabilization axe developed. To illustrate the validness of the theoretic results, many numerical examples axe worked out.

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

A nonlinear pulse systems with a time-variant continuous linear part is considered. A method for synthesizing an output-feedback robust stabilizing control is suggested.

In this paper, a robust output feedback stabilization for a class of Autonomous Underwater Vehicle (AUV) is investigated. Two cases for, nonlinear, decoupled equations of motion of AUV in steering plane are considered in this work. In the first scenario, where all states are measurable, semi-global asymptotic stability for a class of AUV is shown by proposing a state-feedback controller based on Sliding Mode Control (SMC). The stability analysis is evaluated under model uncertainties and parametric variations. Then for the second case, Extended High-Gain Observer (EHGO), augmented with Extended Kalman Filter (EKF) is used to estimate the immeasurable states. It is shown that the states of the closed-loop system with output feedback controller, approach the invariant manifold in finite time and stay there. Efficacy of the proposed controllers is demonstrated with the help of numerical simulations.

Because the inter-sample behavior can be considered, the lifting technique now becomes the unique method for design and analysis of sampled-data systems. However, when we consider the robust stability problem by using the small gain theorem, the state transition operator is zero, and the current lifting algorithms can not be used directly. The lifting computation formulas for the case of the robust stability analysis are derived in detail. Further study shows that when the lifting technique is used for robust stability analysis, its result is conservative. A new discretization method for robust stability analysis is proposed in the paper, and it is not conservative when the condition of the small gain theorem is used. Two examples are given here to illustrate the above ideas.

Robust stabilization is studied within the context of time-domain feedback control of single-input-single-output distributed parameter systems using approximate models. Using the operational methods of Mikusinski (1983), one can easily obtain strong versions of several famous theorems on robust stabilization. The operational methods of Mikusinski can play a powerful role in control theory. Using these methods, one is able to avoid the technical difficulties of convergence, existence, inversion, etc. associated with the Laplace transform. Unlike similar estimates obtained via the contraction mapping and small gain theorems, one is able to obtain robust stabilization free of restrictions on the size of certain error operators. >

Robust Linear Feedback Control of Attitude for Directional Drilling Tools (13th IFAC Symposium on Automation in Mining, Mineral and Metal Processing)

This paper provides a time-domain feedback analysis of the perceptron learning algorithm and of training schemes for dynamic networks with output feedback. It studies the robustness performance of the algorithms in the presence of uncertainties that might be due to noisy perturbations in the reference signals or due to modeling mismatch. In particular, bounds are established on the step-size parameters in order to guarantee that the resulting algorithms will behave as robust filters. The paper also establishes that an intrinsic feedback structure can be associated with the training schemes. The feedback configuration is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The stability of the feedback structure is then analyzed via the small gain theorem, and choices for the step-size parameter in order to guarantee faster convergence are deduced by using the mean-value theorem. Simulation results are included to demonstrate the findings.

The problem of designing multivariable stabilization controllers that satisfy an optimal condition is considered in this paper. Specifically, it is required to find a robust stabilization controller so that closed-loop stability and asymptotic regulation occur, and also so that a quadratic performance index will be minimized. Necessary and sufficient conditions for a robust optimal output-feedback stabilization are presented. The gradient is considered over a functional defined on matrix spaces. Conditions for an optimal point are derived for this kind of functional. Finally, an algorithm for the robust optimal output-feedback design and an example are given.

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