Sufficient or necessary conditions for modal controllability and observability of Roesser's 2-D system model

Controllability and observability properties of Roesser's 2-D system model have been investigated, and some strong necessary and/or sufficient conditions are found.     

Necessary and sufficient conditions for controllability and observability of switched impulsive control systems

Many practical systems in physics, biology, engineering, and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This note first introduces the impulsive behavior into switched linear systems and studies the controllability and observability of such systems. Necessary and sufficient criteria for reachability and controllability are established. It is proved that reachability is equivalent to controllability for such systems. Then, necessary and sufficient criteria for observability and determinability of such systems are established by duality. It is also proved that observability is equivalent to determinability. Our criteria are of geometric type, they can be transformed into algebraic form conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.     

Direct controllability and observability time domain conditions ofsingular systems

Controllability and observability criteria for singular systems using direct formulas in the time domain are introduced. The method used is based on a direct expansion of the transfer function matrix via a Leverrier-type algorithm. Hence, no decomposition of the state-space model is needed and the criteria are implementable on a digital computer. The compact form of the matrices might be helpful in other analysis as well as synthesis problems in singular systems     

A necessary and sufficient condition for the perspective observability problem

In this paper we derive a necessary and sufficient condition for observing the initial condition of a new class of system known as the perspective system. Such a system has already been applied in the field of computer vision especially in the area of motion estimation problems. Our result generalizes an earlier result by Popov-Belevitch-Hautus on the problem of observing a linear dynamical system.     

On controllability and observability of time delay systems

This paper deals with controllability and observability properties of time delay systems in the state spaceR^{n} times L^{p}. In particular, we prove the equivalence of spectral controllability and approximate null-controllability. Moreover, it is shown that the necessary, condition for approximateF-controllability-obtained recently by Manitius-is also sufficient, and a verifiable and matrix type criterion forF-controllability is derived for systems with commensurate delays. Finally, we introduce the dual observability notion of approximate controllability and prove that the control system Σ is exactly null-controllable if and only if the transposed delay system Σ^Tis continuously finally observable.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.     

On the controllability and observability of composite systems

Necessary and sufficient conditions for a linear multivariable feedback composite system to be completely controllable and completely observable are derived. The present derivation also provides a simple proof of the Hsu-Chen Theorem.     

Second-order conditions for local controllability

This paper presents second-order (depending on the 2-jet) sufficient conditions for small time local controllability of affine smooth control systems, based on a very simple observation that can also lead to higher-order conditions; a second-order obstruction for a certain class of systems is also discussed, as is the gap between the obstruction and the sufficient condition. The new results are used for deciding local controllability of systems for which a direct application of the usual criteria is not conclusive.     

Efficient algorithm for determining controllability and observability of large-scale composite systems

The investigation of controllability and observability of large composite systems requires the determination of the rank of large sparse matrices. A computationally efficient algorithm is presented, which is based on the application of reduced outer products for transforming the matrix into an upper triangular form.     

Robust controllability and observability degrees of polynomially uncertain systems

This paper deals with the class of polynomially uncertain continuous-time linear time-invariant (LTI) systems whose uncertainties belong to a semi-algebraic set. The objective is to determine the minimum of the smallest singular value of the controllability or observability Gramian over the uncertainty region. This provides a quantitative measure for the robust controllability or observability degree of the system. To this end, it is shown that the problem can be recast as a sum-of-squares (SOS) problem. In the special case when the uncertainty region is polytopic, the corresponding SOS formulation can be simplified significantly. One can apply the proposed method to any large-scale interconnected system in order to identify those inputs and outputs that are more effective in controlling the system, in a robust manner. This enables the designer to simplify the control structure by ignoring those inputs and outputs whose contribution to the overall control operation is relatively weak. A numerical example is presented to demonstrate the efficacy of the results.     

Model matching systems: necessary and sufficient conditions for stability under plant perturbations

Necessary and sufficient conditions of robust stability are derived for multivariate perfect model matching systems under external disturbances and plant perturbations (non-linear, linear feedback perturbations and fractional perturbations). The derived results also provide an intuitive insight into controller effects on robustness. A general parametrized 2-D controller is introduced to stabilize the nominal plant.     

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.     

On the controllability and observability of discrete-time linear time-delay systems

This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.     

The robustness of controllability and observability of linear time-varying systems

Fixed point methods from nonlinear analysis are used to establish conditions under which the uniform complete controllability, of linear time-varying systems is preserved under nonlinear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under nonlinear perturbation in the state dynamics and output read-out map. Robustness of partial controllability., observability, and a specific kind of nonzero input observability are also proven.     

On the concepts of controllability and observability of linear systems

The objectives of this paper are to give a self-contained presentation of the subject of "controllability" and "observability" (concepts due to Kalman) developed in a simple yet general and rigorous way; to introduce these concepts in terms of the output as well as in terms of the state; and to point out and illustrate some of the subtleties which exist in the time-varying case.     

Modal characterizations of controllability and observability in time delay systems

New characterizations of controllability and observability in linear, time-invariant time delay systems are derived. An explicit criterion for stabilizability in terms of system parameters is obtained. Applications of these results are indicated.     

Signal insensitivity, controllability, and observability in linear systems

Signal insensitivity, suitably defined in terms of Frèchet derivative, is proved to be equivalent to signal invariance in linear time-invariant systems. Then, relations between signal-insensitivity and controllability-observability properties of the system are briefly reviewed.     

When does the local controllability of the general model of 2-D linear systems imply its local reachability?

A relationship between the local controllability of the general model of two-dimensional linear systems and its local reachability is considered. Sufficient conditions are established under which the local controllability of the general model implies its local reachability.