Aa Anton Stoorvogel

The robust H/sub 2/ control problem: a worst-case design

The worst-case effect of a disturbance system on the H/sub 2/ norm of the system is analyzed. An explicit expression is given for the worst-case H/sub 2/ norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L/sub 2/-induced operator norm. An upper bound for this measure, which is equal to the worst-case H/sub 2/ norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature. >

Fundamental problems in fault detection and identification

A number of different fundamental problems in fault detection and fault identification are formulated in this paper. The fundamental problems include exact, almost, generic and class-wise fault detection and identification. Necessary and sufficient conditions for the solvability of the fundamental problems are derived. These conditions are weaker than the ones found in the literature since we do not assume any particular structure for the residual generator. At the end of the paper, a time domain synthesis procedure based on state-space methods to construct appropriate residual generators is given. Copyright

A reduced order observer based controller design for H/sub /spl infin//-optimization

In this note the H/sub /spl infin// control problem with measurement feedback is investigated. It is well-known that for this problem, in general, we need controllers of the same dynamic order as the given system. However, in the case that some entries of the measurement vector are not noise-corrupted, we show that one can find dynamic compensators of a lower dynamical order. Note that this implies that the standard assumptions on the direct feedthrough matrices, as made in most papers on H/sub /spl infin// control, are not satisfied. Our result can be derived by using reduced order observer based controllers. >

On simultaneous global external and global internal stabilization of critically unstable linear systems with saturating actuators

This paper deals with simultaneous global external as well as global internal stabilization of linear systems with saturating actuators. The paper proposes a new family of scheduled low-and-high gain state feedback laws that yields a closed-loop system that is both globally finite gain L/sub p/ stable and globally asymptotically stable. Moreover, the controller has an explicit design parameter that can be adjusted to make the L/sub p/ gain of the closed-loop system arbitrarily small.

Constrained stabilization problems for linear plants

Linear systems with magnitude and rate constraints on both the state and control variables are considered. For such systems, semi-global and global constrained stabilization problems are formulated when state feedback controllers are used. Necessary and sufficient conditions for the solvability of the formulated problems are developed. Moreover, design methodologies for such constrained stabilization problems are presented. An important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved.

The singular H 2 control problem

In this paper we discuss the standard H2 control problem for linear, finite-dimensional, time-invariant systems without any assumptions on the system parameters. We give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained.

Output regulation of linear plants with actuators subject to amplitude and rate constraints

We consider semi-global stabilization and output regulation problems via state and measurements feedback for linear plants (both continuous-time and discrete-time) with actuators subject to amplitude and rate saturation. In our approach, the actuator constraints are modelled as an operator and is incorporated in the controller so that the control signal does not overload the actuators. Both the problem formulation and the analysis is done in the functional differential equation framework.

Nonlinear L/sub 1/ optimal controllers for linear systems

In this paper we study the L/sub 1/ optimal control problem for linear systems. We show that by allowing the class of controllers to include nonlinear controllers, we can make the closed-loop L/sub 1/ norm strictly smaller than we could do using only linear controllers. >

The disturbance decoupling problem with measurement feedback and stability for systems with direct feedthrough matrices

In this paper the known geometric results on the disturbance decoupling problem with measurement feedback and internal stability (DDPMS) are extended to include non-zero direct feedthrough matrices. Necessary and sufficient conditions for the solvability of the DDPMS are expressed in terms of three subspace inclusions.

THE DISCRETE ALGEBRAIC RICCATI EQUATION AND LINEAR MATRIX INEQUALITY

We study the discrete time algebraic Riccati equation. In particular we show that even in the most general cases there exists a one-one correspondence between solutions of the algebraic Riccati equation and deflating subspaces of a matrix pencil. We also study the relationship between algebraic Riccati equation and the discrete time linear matrix inequality. We show that in general only a subset of the set of rank-minimizing solutions of the linear matrix inequality correspond to the solutions of the associated algebraic Riccati equation, and study under what conditions these sets are equal. In this process we also derive very weak assumptions under which a Riccati equation has a solution.