Pole assignment for uncertain systems in a specified disk by output feedback

Robust linear controller design of uncertain discrete systems with time-varying delay

The authors present a sufficient condition for quadratic stabilizability of uncertain linear discrete time systems using LQ (linear quadratic) regulators. The true system is represented by a nominal model plus additive terms representing the uncertainties in the state and input matrices. With a proper choice of these terms, one may represent the most common types of uncertainties encountered in the literature. The main result of the present work is a robustification procedure for discrete time LQ regulators, which is based on a sufficient condition for quadratic stabilizability. The conservativeness of the proposed condition is discussed and some examples are given. >

: This report considers a feedback control law for linear time-varying and time invariant discrete systems based on a receding horizon concept applied to a minimum energy problem with fixed terminal constraints. The control law is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems as well as extending some well known methods for stabilizing time invariant systems. In particular, the stabilizing gains of the feedback control law are obtained from the solution to a discrete Riccati equation over an arbitrary finite time interval, which is relatively easy to compute. The gain matrix reduces to a constant matrix for linear time invariant systems. Some stability results will turn out to be special cases of these results. The results parallel those for linear continuous time systems, although the technical details are tedious and more involved.

Conditions for the solvability of the discrete Lyapunov and the discrete Riccati equations subject to linear equality constraints are derived. These problems arise naturally in the context of output min-max robust control. It is shown that the following problems are equivalent to one another: (a) the solvability of the constrained discrete Riccati equation; and (b) the existence of a feedback gain that guarantees the solvability of the constrained discrete Lyapunov equation of the resulting closed loop. A simple criterion for the existence of a solution to both problems is presented. These problems are shown to be related to the discrete positive real property.

H In this paper we address the problems of robust stability and robust perform2 ance for uncertain discrete time systems with nonlinear parametric uncertainties. We consider two families of systems with parametric uncertainties described by state-space models which offer a fairly general representation of most uncertain systems with one or two parameters (the approach can be extended to more parameters). For these two families we obtain explicit expressions for the Schur stability H radius and for the robust performance radius in the case of uncertainties with a 2 single parameter. Moreover, we provide a line search algorithm for these two problems in the case of two parameters. Both for the robust stability and the robust performance problem, explicit necessary and sufficient conditions are derived.

A new sufficient condition is proposed for robust root clustering in an arbitrary subregion of the complex plane for both linear continuous time and linear discrete time uncertain systems. The systems are described by state space models with structured parameter uncertainty. Explicit bounds on uncertain parameters are derived to guarantee root clustering inside any specified region which may be demanded by stability and performance robustness. Illustrative examples show that the results of the proposed method can be much less conservative compared with the results of existing methods

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.

A higher-order integrator approach is proposed to obtain an approximate discrete-time transfer function for uncertain continuous systems having interval uncertainties. Thanks to simple algebraic operations of this approach, the resulting discrete model is a rational function of the uncertain parameters. The problem of non-linearly coupled coefficients of exponential nature in the exact discrete-time transfer function is therefore circumvented. Furthermore, interval structure of the uncertain continuous-time system is preserved in the resulting discrete model by using this approach. Formulas to obtain the lower and upper bounds for the discrete interval system are derived, so that existing robust results in the discrete-time domain can be easily applied to the discretized system. Digital simulation and design for the continuous-time interval plant can then be performed based on the obtained discrete-time interval model.

This work investigates the problem of designing robust $\mathcal{H}_{\infty}$ static output-feedback controllers for uncertain linear discrete time-invariant systems where all matrices are supposed to be affected by polytopic uncertainties. The proposed control law employs a fixed number of past measured outputs, thus enhancing the dynamics of the closed-loop system and producing controllers with memory. The method for synthesizing the memory controllers relies on a two-phase algorithm. In the first phase a parameter-dependent state-feedback gain is designed and, then, it is used as input to the second phase in which the robust memory static output-feedback controller is synthesized. Numerical examples illustrate the advantages of the proposed approach in terms of $\mathcal{H}_{\infty}$ performance when compared to other methods available in the literature.

Robust D-stability analysis for linear uncertain discrete singular systems with state delay

Optimal fault detection for linear discrete time-varying systems

The problem of guaranteed cost control for a class of linear discrete uncertain system is considered. The system under consideration contains convex polyhedral uncertain parameters. An upper bound of the performance measured by standard quadratic function is constructed, and a method of designing state feedback robust stabilizing control law guaranteeing this quadratic performance index of system to be less than this upper bound is derived. It is proved that whether such a control law exists is equivalent to the feasibility of a group of linear matrix inequality. Also, a procedure is given to select an optimal state feedback controller in the sense of minimizing the upper bound of quadratic performance index.

Consideration was given to the linear-quadratic problem of optimal control for the discrete linear system with fast and slow variables under incomplete information about system state. Decomposition of the discrete matrix Riccati equations was carried out. The proposed decomposition algorithm relies on a geometrical approach using the properties of the invariant manifolds of slow and fast motions of the nonlinear multirate discrete systems as basis. The splitting transformation was constructed in the form of asymptotic decomposition in the degrees of a small parameter.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

For singular networked control systems (SNCSs) with uncertain time-delay, the problem of robust control is studied.The SNCS can be modeled as a class of uncertain discrete linear system with uncertain delay. Sufficient condition, which ensures the resulted loop-system to be asymptotic stability with performance index , is derived.Furthermore, the explicit formation of dynamical output feedback controller is also presented.Finally, a numerical example is given to show the effective of the presented method.