Control Of Uncertain Discrete-time Systems Research Articles

Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays

The guaranteed cost control problem is studied in this paper for a class of uncertain linear discrete-time systems with both state and input delays and a given quadratic cost function. The uncertainty in the system is assumed to be norm-bounded and time-varying. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach, a parametrized characterization of the guaranteed cost controllers (if they exist) is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Robust H∞ control for uncertain discrete-time systems with circular pole constraints

This paper investigates the problem of robust H ∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H ∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H ∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H ∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H ∞ control and robust pole assignment of uncertain systems.

Robust guaranteed cost control for discrete-time uncertain systems with delay

The uncertain systems under considered depend on norm-bounded time-varying matrices of uncertain parameters. The authors develop a quadratic guaranteed cost control method for robust stabilisation via linear memoryless state feedback and static output feedback. Also presented is a robust state feedback controller and static output feedback controller. It is shown that the state feedback controller and output feedback controller can be constructed by solving a linear matrix inequality.

Robust adaptive control of uncertain discrete-time systems

In this paper, a robust adaptive controller for a class of nonlinear uncertain discrete-time systems is developed by combining the backstepping procedures with a simple parameter estimator subject to parameter projection. It is shown that the proposed controller can ensure boundedness of all signals in the overall adaptive systems in the presence of unmodelled dynamics and disturbances. It can also guarantee that the tracking error is bounded by a function of the size of the unmodelled dynamics. In the ideal case when there are no unmodelled dynamics and disturbances, perfect tracking is ensured.

Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters

In this paper, we first study the problems of robust quadratic mean-square stability and stabilization for a class of uncertain discrete-time linear systems with both Markovian jumping parameters and Frobenius norm-bounded parametric uncertainities. Necessary and sufficient conditions for the above problems are proposed, which are in terms of positive-definite solutions of a set of coupled algebraic Riccati inequalities. Then, the problem of robust quadratic guaranteed cost control for the underlying systems is investigated. A guaranteed cost control is designed to ensure the cost function is within a certain bound, irrespective of all admissible uncertainities. © 1998 John Wiley & Sons, Ltd.

Quadratic guaranteed cost and disc pole location control for discrete-time uncertain systems

The paper deals with quadratic guaranteed cost control with pole placement in a disk. The objective is twofold: first to translate to discrete-time systems previous results for continuous-time systems. It is shown that in the two cases (discrete and continuous time), the procedures to design a state feedback control which places the poles in a disc and ensures a performance level through a linear quadratic criterion are formally identical. It consists of solving an optimisation problem. The second important point is to show that the criterion in this optimisation problem is convex with respect to ε and then a global optimal solution is reachable by a one-line search algorithm.

Minimax optimal control of discrete-time uncertain systems with structured uncertainty

Inthis paper we consider a guaranteed cost control problem fora class of uncertain discrete-time systems which contain structureduncertainties. The uncertainties are assumed to satisfy a certainsum quadratic constraint. The controller will be a minimax controllerin the sense that it minimizes the maximum value of a cost function.For a given initial condition, the minimax optimal controlleris constructed by solving a parameter dependent Riccati equation.This controller guarantees absolute stability of the closed loopsystem.

On the ℒ/sub 1/ norm of uncertain linear systems

In this paper we present an algorithm for computing the l/sub /spl infin//-induced norm of linear systems described by time-varying difference equations with uncertain system matrices. The approach is based on ideas from convex analysis. The convergence of the algorithm is studied, and vertex-type results related to the stabilization and /spl Lscr//sub 1/-control of uncertain discrete-time systems are established. >

H/sub ∞/ control of discrete-time uncertain systems

This paper considers H/sub /spl infin// control problems involving discrete-time uncertain linear systems. The uncertainty is supposed to belong to convex-bounded domains, and no additional assumptions are made (as, for instance, matching conditions). Two H/sub /spl infin// guaranteed cost control problems are solved. The first one concerns the determination of a state feedback gain (if one exists) in such way the H/sub /spl infin// norm of a certain transfer function remains bounded by a prespecified H/sub /spl infin// level for all possible models. The second one includes this bound as an additional variable to be minimized to achieve the smallest feasible limiting bound. The results follow from the simple geometry of those problems which are shown to be convex in the particular parametric space under consideration. An example illustrates the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions

In this note, linear discrete-time systems affected by both parameter and input uncertainties are considered. The problem of the synthesis of a feedback control, assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. It is shown that the problem has a solution if and only if there exists a certain Lyapunov function which does not belong to a preassigned class of functions (e.g., the quadratic ones), but it is determined by the target set in which ultimate boundedness is desired. One of the advantages of this approach is that we may handle systems with control constraints. No matching assumptions are made. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. The resulting compensator may be implemented as a linear variable-structure control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>