Masami Saeki

Method of robust stability analysis with highly structured uncertainties

This paper presents a method of analyzing the stability of linear time-invariant interconnected systems with uncertainties: each subsystem is single-input single-output and its vector locus lies inside a polygon at each frequency. It is shown that the convex closure of the image of the Cartesian product of these polygons under the mapping \phi = \det [I + FH] agrees with the convex closure of the image of the vertices of these polygons under the mapping φ. From this result the image can be estimated by a finite Dumber of calculations. A sufficient stability condition is obtained by applying this result to the multivariable Nyquist stability criterion.

H∞ control with pole assignment in a specified disc

In this paper, a method of pole assignment in H ∞ control theory is proposed. By this method, all the poles can be placed in a left half-plane or inside a disc on the complex plane and at the same time an H ∞ norm constraint is satisfied. This result can be derived by a bilinear transformation of the complex variable of a transfer function in H ∞ control theory

H ∞ /LTR procedure with specified degree of recovery

This paper presents a new Loop Transfer Recovery procedure which recovers a robustness property at plant inputs to a specified degree. It is pointed out that generally the controller obtained by LTR method is stable. A difference between the open loop transfer function of a state feedback system by LQ regulator and that of an output feedback system by LQ regulator with observer is estimated quantitatively by H∞ norm. A design problem of full/minimal order observers for which the norm is less than a specified value is proposed. This problem is reduced to an H∞optimal control problem with state feedback. The design procedure is applicable to not only minimum phase plants but also non-minimum phase plants. The relation between this method and LQG/LTR method is examined.

Application of a new stability criterion of composite systems to multimachine power systems

A new stability criterion of composite systems is applied to multimachine power systems. This criterion has advantage in evaluating the influence of the interaction by bilinear forms. In the examples, it is shown that the range of the values of parameters for which the new method can assure stability is considerably wider than that obtained by the Jocic et al. method.

Stability margin calculation for systems with structured time-delay uncertainties

A method of calculating a stability margin of systems with uncertain time-delay elements is presented. This method utilizes the bilinear transformation of time-delay elements to obtain a multilinear function in order to compute the stability margin by applying the mapping theory proposed for the robust stability test. >

Methods of solving a polynomial equation for an H/sub infinity / optimal control problem for a single-input single-output discrete-time system

A polynomial equation for the H/sub infinity / optimal control problem is reduced to a nonlinear algebraic equation. Two methods are proposed for solving the algebraic equation. One method uses the singularity of a linear algebraic equation as the optimality index. The other gives an approximate solution by solving an eigenvalue problem. A numerical example is presented. >

CAD package for control system on Mathematica

A new computer-aided design (CAD) package for the design of control systems is developed. A kernel and front-end structure is employed in the package. The symbolic computation system Mathematica is embedded in the CAD package, enabling the package to perform symbolic computation. The effectiveness of the package is confirmed by a design example.<<ETX>>

Search method for the weighting matrix of the weighted multivariable circle criterion

The weighted multivariable circle criterion contains an arbitrary diagonal matrix that is called the ‘weighting matrix’. In this paper, a method of searching for an adequate weighting matrix is proposed. The choice of the weighting matrix determines the sharpness of the stability criterion obtained. The method is based on the relation between an M-matrix and a positive-definite hermitian matrix. The results of examples show that this method is very useful in obtaining sharper stability conditions.

Search methods for a constant scaling matrix attaining minimum H/sup infinity / norm

The authors propose two iterative methods of searching for a constant diagonal matrix W>0 for which the H/sup infinity / norm of W/sup 0.5/G(s) W/sup -0.5/ takes minimum value. One method uses an M-matrix property on a frequency domain and the other a Riccati equation property in a state space. Numerical examples show that the convergence is stable and quick within a few iterations by the frequency-domain approach, and that the convergence is within several iterations for an appropriately chosen step length by the state-space approach.<<ETX>>

Search method for the matrix multiplier time constant and the weighting matrix of the multivariable Popov stability criterion

The multivariable Popov stability criterion contains two arbitrary diagonal matrices which are called the weighting matrix and the multiplier time constant matrix. The choice of the matrices determines the sharpness of the stability criterion obtained. In this paper, a method of searching for adequate values of the matrices is proposed. The method is based on the relation between the M-matrix and the positive-definite hermilian matrix. Numerical examples show that this method is useful in obtaining a sharper stability condition.