H∞ control of discrete-time uncertain linear systems with quantized feedback

This paper presents a new dilated linear matrix inequality (LMI) representation to design a state feedback controller and a dynamic feedforward disturbance compensator for linear parameter-varying (LPV) systems. The improved LMIs are convex and finite-dimensional without any iterative approach. The designs are based on a new proposed equivalent bounded real lemma (BRL) by means of matrix dilation for LPV systems and uncertain linear systems under time-varying parametric uncertainties (TVPUs). This dilated BRL provides lower conservative results than existing methods in terms of robust stability. Accordingly, a dynamic disturbance compensator is designed in addition to a state feedback controller. This paper mainly focuses on the design of compensators against disturbances in addition to the design of state feedback controllers. The dynamic matrices of the compensator change with the time-varying parameters of the LPV or uncertain system during operation, assuming that the disturbances and the parameters are measurable or observable. The compensator can be designed to attenuate the disturbances/noises or to improve reference tracking. Finally, numerical and simulation outcomes are presented to prove both the effectiveness and lower conservativeness of the proposed LMIs.

In this paper, a class of discrete-time uncertain linear hybrid systems, which is affected by both parameter variations and exterior disturbances, is considered. The goal here is to synthesize a hybrid control law, which includes the continuous variable control law and the discrete event control signal, so as to guarantee the controlled invariance for a specific region in the hybrid state space. It turns out that the continuous variable control law is a piecewise linear state feedback control based on the partition of the given region's continuous variable state space projection. A numerical example is given for illustration.

This paper considers a subclass of hybrid systems, which is the discrete-time linear switching systems whose changes in the dynamics are determined by exogenous, uncontrollable events, and resets are present. In the presence of uncertain parameter and non-symmetrical constrained control, based on the results of nominal linear switching systems, a necessary and sufficient condition to test the robustness of a state feedback controller is given. The candidate state feedback controller for this test is that stabilizing nominal discrete-time linear switching systems. Also, the method in this paper can be extended to the case which has state constraints. At last, a numerical example is presented to illustrate the technique.

Stabilization of fractional-order singular uncertain systems

Studies the optimal guaranteed control problem for a class of linear uncertain time-delay systems. The systems under consideration are described by state differential equations with time-varying unknown but norm-bounded uncertain parameters and time-varying unknown but bounded delay in states. An upper bound of the performance measured by standard quadratic function is constructed and based on the delay-dependent stabilizing approach, a method of designing a state feedback robust quadratic stabilizing control law guaranteeing this quadratic performance index be less than the constructed upper bound is derived. A procedure is given to select an optimal state feedback controller in the sense of minimizing this upper bound of the quadratic performance index. The results depend on the size of delay and are given in terms of several linear matrix inequalities.

This paper is concerned with the robustness and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem of observer-based control for a class of uncertain linear discrete-time systems with both state and input delays. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear Matrix Inequality(LMI) optimization approach is used to design the observer-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control. An example illustrates the application of the proposed technique.

The robust stabilization problem for a class of uncertain linear time-delay systems containing sector saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. The new criterion of delay-dependent robust stabilizability for uncertain time-delay systems is presented and the corresponding robust memoryless state feedback controller is derived in terms of the solutions of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

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Robust H∞ control for uncertain discrete-time state-delayed linear systems with markovian jumping parameters

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

In this paper, the finite-horizon near optimal adaptive regulation of linear discrete-time systems with unknown system dynamics is presented in a forward-in-time manner by using adaptive dynamic programming and Q-learning. An adaptive estimator (AE) is introduced to relax the requirement of system dynamics, and it is tuned by using Q-learning. The time-varying solution to the Bellman equation in adaptive dynamic programming is handled by utilizing a time-dependent basis function, while the terminal constraint is incorporated as part of the update law of the AE. The Kalman gain is obtained by using the AE parameters, while the control input is calculated by using AE and the system state vector. Next, to relax the need for state availability, an adaptive observer is proposed so that the linear quadratic regulator design uses the reconstructed states and outputs. For the time-invariant linear discrete-time systems, the closed-loop dynamics becomes non-autonomous and involved but verified by using standard Lyapunov and geometric sequence theory. Effectiveness of the proposed approach is verified by using simulation results. The proposed linear quadratic regulator design for the uncertain linear system requires an initial admissible control input and yields a forward-in-time and online solution without needing value and/or policy iterations. Copyright © 2014 John Wiley & Sons, Ltd.

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