Showing papers by "John B. Moore published in 1967"
01 Dec 1967
TL;DR: In this article, the authors apply the results of this optimal control theory to a class of problems in which the feedback law is realized by a linear dynamical system, where the quadratic loss function of interest in this case consists of terms involving time derivatives of the input vector as well as the usual terms involving the input and state vectors.
Abstract: A very significant result in modern control theory is that, for a linear, finite-dimensional, dynamical system, the state feedback law derived from a quadratic-loss-function minimisation problem is linear. The paper applies the results of this optimal control theory to a class of problems in which the feedback law is realised by a linear dynamical system. The quadratic loss function of interest in this case consists of terms involving time derivatives of the input vector as well as the usual terms involving the input and state vectors. Optimal control problems of this type may arise, for example, when the input force or energy is to be included in the cost terms of the performance index. An advantage of the controllers resulting from the optimisation procedure is that they are dynamic, and thus possess finite bandwidth; accordingly they can be used when there is a limitation to the bandwidth of a communication channel over which feedback signals are transmitted.
24 citations
01 Apr 1967
TL;DR: In this paper, the zero of polynomials with real or complex coefficients was determined using steepest descent method in convergent procedure, where the coefficients were assumed to be real and complex.
Abstract: Zeros of polynomials with real or complex coefficients determined, using steepest descent method in convergent procedure
18 citations
TL;DR: In this article, the lemma of Lyapunov is generalized for time-varying systems, in which it is shown that additional conditions are required for the lemmas to hold.
Abstract: The lemma of Lyapunov gives the necessary and sufficient condition for the stability of a time-invariant system in terms of the existence of a positive-definite symmetric matrix. In this letter, the lemma is generalised for time-varying systems, in which it is shown that additional conditions are required for the lemma to hold. The conditions involve boundedness of certain quantities and uniform complete observability of a pair of matrixes.
16 citations
01 Oct 1967
TL;DR: In this article, a system theory description alternative to those already known for transfer function matrices which are positive real is presented using the fact that the transpose of a positive real matrix is itself positive real.
Abstract: Systems theory descriptions alternative to those already known are presented for transfer function matrices which are positive real. They are derived using the fact that the transpose of a positive real matrix is itself positive real.
13 citations
TL;DR: Nominally linear optimal-control regulating systems are examined and it is found that a large degree of nonlinearity will not disturb the stability of the system.
Abstract: Nominally linear optimal-control regulating systems are examined with a view to assessing the amount of nonlinearity which can be tolerated in the input transducer. Using a suitable Lyapunov function, it is found that a large degree of nonlinearity will not disturb the stability of the system.
10 citations
TL;DR: Two classes of systems are considered for the application of the multivariable Popov criterion and it is shown that it is always it is possible to tolerate in general a small amount of non-linearity at virtually any point in the system without impairment of stability.
Abstract: Two classes of systems are considered for the application of the multivariable Popov criterion The first is obtained from a linear, finite-dimensional system with a state feedback law derived from a quadratic loss function minimization problem It is shown that a non-critical part of the system is the set of transducers producing the inputs to the system, in the sense that stability is retained even when the transducers are far from ideal The second class of systems is derived from linear, finite-dimensional systems which are stable It is shown that it is always it is possible to tolerate in general a small amount of non-linearity at virtually any point in the system without impairment of stability
7 citations
TL;DR: An algorithm is given to be used in conjunction with the parameter-plane method and the describing-function method for rapid calculation of transient oscillations in the design of a class of nonlinear systems.
Abstract: An algorithm is given to be used in conjunction with the parameter-plane method and the describing-function method for rapid calculation of transient oscillations in the design of a class of nonlinear systems.
3 citations
TL;DR: The Popov criterion for the stability of linear, time-invariant, finite-dimensional systems with a single nonlinearity has been generalized by a number of authors through a relaxation of the single non-linearity and the finite dimension constraints in order to be applicable to a wider range of practical problems.
Abstract: The Popov criterion for the stability of linear, time-invariant, finite-dimensional systems with a single non-linearity has been generalized by a numbers of authors through a relaxation of the single non-linearity and the finite-dimensional constraints in order to be applicable to a wider range of practical problems. This paper extends these results further by relaxing the time-invariant constraint. It is shown that a covariance condition when satisfied is a sufficient condition for the system output to be bounded and square integrable for zero input conditions.
1 citations