Delay-Dependent Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Switched Delay Systems

In this paper, we study stability analysis and stabilization problems for a class of nonlinear two-dimensional (2-D) discrete systems with time-varying state delays, described by local state-space (LSS) Fornasini-Marchesini (FM) second model. The upper and lower bounds of time-varying state delays are positive integers and the nonlinearity satisfies Lipschitz condition. First, a stability criteria is proposed through introducing a new Lyapunov function. Then a dynamic output feedback controller is designed to assure the stability of nonlinear 2-D time-varying systems. Moreover, the output feedback system matrices can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of our results.

This paper considers the output feedback guaranteed cost controller design problem for uncertain discrete-time systems. The uncertainty is assumed to be of linear fractional form, unstructured, and is allowed to be time-varying. It is proved that the existence of a guaranteed cost controller is equivalent to the feasibility of a certain linear matrix inequality (LMI), and that a full-order output feedback controller can be constructed in terms of the feasible solution to the LMI. Furthermore, a convex optimization problem is introduced for the selection of a suitable controller minimizing a specified cost bound.

Output Feedback Guaranteed Cost Control for Linear Uncertain System with Input Saturation

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.

The robust passivity synthesis problem is addressed for a class of uncertain delayed systems with time-varying delays in both state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all the matrices of the model. The problem aims at designing an observer-based dynamic controller that renders the closed-loop systems strongly robustly stable with strictly passive for all admissible uncertainties, dependently of the maximum of delay derivative. By converting the problem at present into a class of strongly stable with strictly passive control problem for some parameterized systems equivalently, the explicit solution is established and expressed in terms of a linear matrix inequality.

This paper is devoted to the problems of non-fragile H∞ and L2–L∞ control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ (or L2–L∞) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov–Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method.

This article aims to investigate the problem of robust finite-time output feedback $$ H_\infty $$H? control for stochastic jump systems with incomplete transition rates. Firstly, for the nominal stochastic jump systems, the sufficient conditions for the finite-time boundedness and finite-time output feedback stabilization are developed, respectively. Then, a robust finite-time $$ H_\infty $$H? output feedback controller is designed by means of linear matrix inequalities. A key point of this work is to relax the special requirement of completely known transition rates to more general form that mixes two cases of completely known and completely unknown transition rates. Finally, a numerical example is given to demonstrate the applicability of the main results.

In this paper, we address a synthesis problem of the parameter-dependent output feedback H∞ control for linear parameter-varying systems with time-delay. The scheme adopts the parameter-dependent past state information to construct the dynamic output feedback controller. In this case, on basis of the quadratic Lyapunov functional with parameter-dependence, we analyze the parameter-dependent H∞ stability conditions for the closed-loop time-delayed linear parameter-varying system in terms of linear matrix inequalities. However, this stability condition is of an infinite-dimension. To derive computationally tractable criteria for the dynamic output feedback controller, several slack variables and a convex relaxation technique are employed to have the infinite-dimensional condition of linear matrix inequalities cast into a finite dimensional convex optimization problem. By solving the convex optimization problem, we harvest the dynamic output feedback controller with memory for the time-delayed linear parameter-varying system. Finally, two examples are included to illustrate the effectiveness of the proposed approach.

This paper is concerned with the output feedback \(\mathcal {H}_\infty \) control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It\(\hat{o}\)-type differential equation with state and disturbance contaminated by white noises. The design of the output feedback \(\mathcal {H}_\infty \) control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback \(\mathcal {H}_\infty \) controller. It is shown that the output feedback \(\mathcal {H}_\infty \) control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton–Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods.

Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions

A robust controller is developed for uncertain, second-order nonlinear\nsystems subject to simultaneous unknown, time-varying state delays and known,\ntime-varying input delays in addition to additive, sufficiently smooth\ndisturbances. An integral term composed of previous control values facilitates\na delay-free open-loop error system and the development of the feedback control\nstructure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals\nguarantees uniformly ultimately bounded tracking under the assumption that the\ndelays are bounded and slowly varying.\n

This paper establishes a framework for stability analysis and memoryless state-feedback control synthesis of linear discrete-time systems with time varying state delay. The underlying idea is converting the considered system into an equivalent constrained switched system, leading to sufficient and necessary condition for stability analysis. Based on this switched system modeling, available information about the time-varying delay such as known bounds of variation rate can be incorporated into the analysis in a natural way. Moreover, sufficient conditions for memoryless state-feedback control design are obtained in a similar style. The analysis and synthesis conditions are given in terms of solvability of a set of linear matrix inequalities (LMIs). Numerical examples are included for illustration.

This paper presents a two-dimensional (2D)-based approach to the problem of output feedback repetitive control for uncertain discrete-time systems. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then sufficient conditions for the existence of output feedback control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal output feedback control law by minimizing the upper bound of a given cost function. Compared with the commonly used 1D-based method, the proposed approach increases the degree of freedom of controller design by not only including in the scheme an output feedback gain but also a feed forward one which can be simultaneously solved using the 2D-based procedures presented in the paper. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Any linear control system, including those with complex structure and dynamic compensation can systematically be formulated as a static output feedback problem where the control system parameters are contained in the output feedback matrix. For this reason, many numerical techniques have been developed specifically to solve the 7/2 optimal ouput feedback problem posed in static output feedback form. Current numerical techniques for computing the output feedback gain matrix recast the problem as a coupled set of Lyapunov equations. Various numerical techniques effectively solve the Lyapunov equations differently. Here, we propose a new numerical method for solving the output feedback gain matrix by direct solution of the cost function using Fade approximation. Using this technique, analytic expressions for cost function derivatives can be written compactly, allowing for efficient solution using second order optimiztion methods. Using a flight control system example, the new method is compared to existing optimal output feedback algorithms.