Constant Linear Control Research Articles

The unconditional stability for the hyperneutral type constant linear control system with delays (I)

By means of the frequency domain method and the inequality analysis, we discuss the unconditional stability problem for the hyperneutral type constant linear control system with delays, and obtain some precise sufficient, sufficient and necessary conditions.

The unconditional stability for the hyperneutral type constant linear control system with delays

In this paper, by means of the frequency domain method and the inequality analysis, unconditional stability problem for the hyperneutral type constant linear control system with delays are discussed, and some precise sufficient, sufficient and necessary conditions are obtained.

The unconditional stability for the multigroup multidelays neutral type linear constant control system

Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.

On the Equivalence Problem of Control Systems and Control Systems with Timelags in the Theory of Stabilization

By the symmetric positive definite solutions of Riccati matrix equation and Riccati differential matrix equation we construct positive definite, quadratic form functions, and give the equivalence of linear constant control systems and linear constant control systems with time-lags, and that of linear time-varying control systems and linear time-varying control systems with time-lags in the theory of stabilizalion. At the same time we obtain the estimate formulae for the bound of the time-lags.

Synthesis of Parameter and State Insensitive Feedback Systems with Constraints Based on Piecewise Constant Linear Control Laws

Linear time-invariant plants x˙¯=A¯x¯+b¯u with given constraints |u(t)|≤uO and |Tw¯ x¯(t)|≤dO are considered. A synthesis procedure appliable hereto (based on applying piecewise constant linear control laws) recently has been described (1). The resulting nonlinear feedback systems are suboptimal with respect to a quadratic performance index and can be realized considerably more easily than optimal systems. Now it is shown, that it is possible to increase the insensitivity of these systems with respect to parameter and state uncertainty by minimizing suitable simple cost functions for every piecewise applied linear control law.

Infinite time optimal control for a class of stochastic systems

Optimization results developed by the author (Brandeberry and Wu 1970) for a class of stochastic regulator problems will be extended from the finite time interval to the infinite time interval. Conditions are given for the existence and stability of the infinite constant feedback of the system state; necessary conditions will also be obtained for the inverse problem (i.e. conditions for a linear constant control law to be optimal for some cost functional).

Greatest common divisor of several polynomials

AbstractGiven a polynomial a(λ) with degree n, and polynomials b1(λ), …, bm(λ) of degree not greater than n – 1, then the degree k of the greatest common divisor of the polynomials is equal to the rank defect of the matrix R = [b1(A), b2(A), …, bm(A)], where A is a suitable companion matrix of a(λ). Furthermore, it is shown that if the first k rows of R are expressed as linear combinations of the remaining n – k rows (which are linearly independent) then the greatest common divisor is given by the coefficients of row k + 1 in these expressions. A simple expression is derived for R and a permutation of the columns of this matrix establishes a direct connexion with controllability of a constant linear control system. Finally, when m = 1 a relationship between the corresponding R and Sylvester's matrix is exhibited.

When Is a Linear Control System Optimal?

The purpose of this paper is to formulate, study, and (in certain cases) resolve the Inverse Problem of Optimal Control Theory, which is the following: Given a control law, find all performance indices for which this control law is optimal. Under the assumptions of (a) linear constant plant, (b) linear constant control law, (c) measurable state variables, (d) quadratic loss functions with constant coefficients, (e) single control variable, we give a complete analysis of this problem and obtain various explicit conditions for the optimality of a given control law. An interesting feature of the analysis is the central role of frequency-domain concepts, which have been ignored in optimal control theory until very recently. The discussion is presented in rigorous mathematical form. The central conclusion is the following (Theorem 6): A stable control law is optimal if and only if the absolute value of the corresponding return difference is at least equal to one at all frequencies. This provides a beautifully simple connecting link between modern control theory and the classical point of view which regards feedback as a means of reducing component variations.