Yoshito Ohta

Reachability, Observability, and Realizability of Continuous-Time Positive Systems

This paper discusses reachability, observability, and realizability of single-input, single-output linear time-invariant systems, in which state variables and/or input (output) functions are restricted to be nonnegative to reflect physical constraints frequently encountered in real systems. We define a set reachable from the origin with nonnegative inputs, and also a set observable with nonnegative outputs. We investigate geometrical structures of the sets through convex analysis, and a duality relation between them is established. Next we consider positive realization of a given transfer function. Using the reachable set and the observable set, we give a necessary and sufficient condition for positive realizability. An example is given to demonstrate that a positive realizable transfer function does not in general have a jointly controllable and observable positive realization.

A necessary and sufficient condition for robust BIBO stability

Abstract This paper is concerned with obtaining necessary and sufficient conditions for robustly stabilizing a class of plants characterized by a known linear shift invariant plant with additive perturbations of the form of possibly nonlinear, time varying l ∞ -stable operators. We will show that, in some sense, the small gain theorem is necessary and sufficient even when the perturbations are restiricted to a class of linear operators.

Unit interpolation in H ∞ : bounds of norm and degree of interpolants

Abstract This paper studies the problem of unit interpolation in H ∞ . Specifically, bounds of the norm and degree of interpolants are obtained using the Nevanlinna-Pick interpolation theory. Also simpler bounds are given using the Poincare metric. These results indicate that strong stabilization and simultaneous stabilization need a cautious approach if the system is ‘ill-conditioned’. In fact, it is demonstrated that the degree of stable compensator is not bounded for the class of plants with fixed degree. Also an example shows that there is a class of plants for which the sensitivity can be made small only if unstable compensators are used.

Rational approximation of L/sub 1/ optimal controllers for SISO systems

The L/sub 1/ optimal control problem with rational controllers for continuous-time systems is considered in which it is shown that the optimal L/sub 1/ performance index with rational controllers is equal to that of irrational controllers. A sequence of rational controllers that approximates the optimal index is constructed. Convergence properties of such a sequence are studied. That the corresponding sequence of objective transfer functions is shown to converge in weak-* topology in BV(R/sub +/) in the time domain and uniformly in a wider sense in the frequency domain. >

Exact Determinations of the Maximal Output Admissible Set for a Class of Nonlinear Systems

This paper is concerned with obtaining necessary and sufficient conditions for fulfilling specified state and control pointwise-in-time constraints against a certain class of nonlinear dynamics. The results are generalizations of the maximal output admissible set theory to the case of nonlinear systems. Main contribution of the present paper is that explicit algorithmic procedures to determine the maximal output admissible set are proposed. Another contribution is that we discuss on a finite determinability of the maximal output admissible set for nonlinear systems. Some relations between observability of nonlinear systems and finite characterizations of the maximal output admissible set are clarified.

Optimal Invariant Sets for Discrete-time Systems: Approximation of Reachable Sets for Bounded Inputs

Abstract Ellipsoidal invariant sets of linear discrete-time systems are treated to approximate the reachable sets for bounded inputs. All the ellipsoids are parameterized by a bilinear matrix inequality. The criteria for the ellipsoids are defined to represent the degrees of approximations. The optimal ellipsoids can be obtained by the convex optimizations with one scalar variable. The efficiency of the proposed method is demonstrated in a numerical example in comparison with a method of previous research.

/spl epsiv/-feasible approximation of the state reachable set for discrete-time systems

This paper considers an approximation problem of the state reachable set for linear discrete-time systems with unknown but bounded exogenous inputs. A simple recursive procedure provides a sequence of enlarging convex polyhedral sets which successively approximates the state reachable set. The main contribution of this paper is to clarify a stopping criterion for the recursive procedure. The notion of positive invariance is utilized to derive the stopping criterion. The procedure makes it possible, as it is contrast to those of other existing methods, to estimate the state reachable set within a required accuracy.

Structural invertibility of transfer functions

In this note, we study certain properties of a transfer function in terms of the structure of the state-space representation ( A, B, C ). Specifically, the rank of the transfer function and the degree of a decoupled system (which can be obtained by applying a left decoupler) are characterized in terms of the structure of ( A, B, C ).

Brief paper: Disturbance rejection with information constraints: Performance limitations of a scalar system for bounded and Gaussian disturbances

This paper derives performance limitations for disturbance rejection of scalar systems under information constraints subject to either bounded or Gaussian disturbances. Two kinds of disturbance are treated in a unified manner, using appropriate entropies and distortions. It is shown that the achievable performance cannot be improved even if the maximum information constraint is relaxed to an average information constraint. Another observation is that, while the information constraints are weaker than bit-rate or signal-to-noise ratio constraints on the communication channel, the same performance levels are achieved by the best encoder and decoder for disturbance rejection with the information constraints.

Realization of input–output maps using generalized orthonormal basis functions

Abstract This paper studies the input–output equivalent transformation (or Hambo transform) of linear time-invariant systems induced by generalized orthonormal basis functions. Transformation formulae of the system matrices are derived using the fact that the lifted system associated with the inner function which defines a generalized orthonormal basis is an abstract form of the Hambo transform. The new formulae are supplements to the results in the literature, and they are equally applicable to continuous-time and discrete-time systems and MIMO and SISO systems.