Squaring down of general MIMO systems to invertible uniform rank systems via pre- and/or post-compensators

Pre- and/or post-compensators are designed to square down a general MIMO system to a uniform rank system, the structure of which is almost similar to a SISO system. The method of squaring down either does not change the finite zero structure of the given MIMO system or simply adds additional finite zeros in the left half s-plane. The significance of such a squaring down lies in the simplicity of the structure of a uniform rank system lending itself for easy analysis and control design.     

Semi‐global stabilization of discrete‐time systems subject to non‐right invertible constraints

This paper investigates time‐invariant linear systems subject to input and state constraints. We study discrete‐time systems with full or partial constraints on both input and state. It has been shown earlier that the solvability conditions of stabilization problems are closely related to important concepts such as the right invertibility or non‐right invertibility of the constraints, the location of constraint invariant zeros, and the order of constraint infinite zeros. In this paper, for general time‐invariant linear systems with non‐right invertible constraints, necessary and sufficient conditions are developed under which semi‐global stabilization in the admissible set can be achieved by state feedback. Sufficient conditions are also developed for such a stabilization in the case where measurement feedback is used. Such sufficient conditions are almost necessary. Controllers for both state feedback and measurement feedback are constructed as well. Copyright © 2009 John Wiley & Sons, Ltd.     

Inverse filtering and deconvolution

This paper studies the so‐called inverse filtering and deconvolution problem from different angles. To start with, both exact and almost deconvolution problems are formulated, and the necessary and sufficient conditions for their solvability are investigated. Exact and almost deconvolution problems seek filters that can estimate the unknown inputs of the given plant or system either exactly or almostly whatever may be the unintended or disturbance inputs such as measurement noise, external disturbances, and model uncertainties that act on the system. As such they require strong solvability conditions. To alleviate this, several optimal and suboptimal deconvolution problems are formulated and studied. These problems seek filters that can estimate the unknown inputs of the given system either exactly, almostly or optimally in the absence of unintended (disturbance) inputs, and on the other hand, in the presence of unintended (disturbance) inputs, they seek that the influence of such disturbances on the estimation error be as small as possible in a certain norm (H₂ or H_∞) sense. Both continuous‐ and discrete‐time systems are considered. For discrete‐time systems, the counter parts of all the above problems when an ??‐step delay in estimation is present are introduced and studied. Next, we focus on the exact and almost deconvolution but this time when the uncertainties in plant dynamics can be structurally modeled by a Δ‐block as a feedback element to the nominally known plant dynamics. This is done either in the presence or absence of external disturbances. Copyright © 2001 John Wiley & Sons, Ltd.     

Output regulation of discrete‐time linear plants subject to state and input constraints

Discrete‐time output regulation of linear systems with state and/or input constraints on magnitude is considered. Structural properties of linear plants are identified under which the so‐called constrained semi‐global and global output regulation problems are solvable. As in the case of continuous‐time systems, an important aspect of our development is a taxonomy of constraints showing a clear relationship between the constraint types and the output regulation results. Solvability conditions are developed for semi‐global and global output regulation problems. Appropriate regulators are constructed for problems that are solvable. Copyright © 2003 John Wiley & Sons, Ltd.     

A note on obtaining reduced order optimal control problems by singular perturbations

This note considers two methods of obtaining reduced order problems (by singular perturbations) in optimal control theory and shows that both methods lead to the same set of equations.     

Computation of the recoverable region and stabilisation problem in the recoverable region for discrete-time systems

This article considers discrete-time linear time-invariant systems subject to input and state constraints. It is shown that in the recoverable region (which is the largest domain of attraction that is theoretically achievable) system can be semi-globally stabilised by nonlinear feedbacks while satisfying the constraints. Moreover, the recoverable region for the given system is constructed by constructing the same, however, for a reduced-order subsystem of the given system. Such a reduction in the order or dimension of the system generally leads to a considerable simplification in the computational effort.     

Exact,almost and optimal input decoupled (delayed) observers

The core of this paper deals with the construction of input-decoupled observers which seek asymptotic estimation of a desired output variable (a linear combination of state and input) of a time-invariant either continuous- or discrete-time system driven by unknown inputs and disturbances. Exact, almost, optimal (suboptimal) and constrained optimal estimation or filtering problems are formulated and studied. All the problems defined and studied here are inherently interconnected, and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals. They are interconnected from a variety of angles, e.g. they are motivated by one another, methods of obtaining the solvability conditions and their methods of solution rely on one another, etc. Thus, a hierarchy of problems and their solutions is built on top of one another. Some of the problems studied here are known in the literature but not in as general a form as is given here, while a majority of the problems studied here are new. A classical variation of all the above problems is also studied here by introducing an l-step delay in estimating the desired output from the measured output. The underlying philosophy throughout this work has been to study most if not all of the facets of estimation and filtering in one stretch under a single folder. Our study of all the above problems has been guided by three important perspectives: (1) obtaining the solvability conditions, both necessary and sufficient; (2) obtaining optimal performance whenever it applies; and (3) developing sound methodologies to design and construct appropriate observers or filters.     

Cheap control problem of a linear uniform rank system: Design by composite control

Cheap control problems where a small parameter μ² multiplies the control cost are considered. Due to the cheapness of control, a strong control action in the form of high-gain feedback forces the given system to have slow and fast, low and high amplitude variations. For a class of linear systems (uniform rank systems), a systematic procedure of amplitude scaling and time-scale decomposition which normalizes high and low amplitude variations and which separates slow and fast time scales is presented. The method permits the explicit characterization of all the limiting properties of the considered cheap control problem as μ → 0. Methods of calculating singular controls and how non-uniqueness can arise in them are discussed. Above all, several suboptimal composite control schemes are developed based on the decomposition of the given optimal design into two lower order subsystem designs.