Method for modelling and analyzing linear time invariant systems with time delays
First Claim
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1. A computer-readable storage medium that comprises computer-executable instructions that when executed perform the method of:
- receiving a first description of a generalized state-space system based on a state-space system, the first description expressing time derivatives of state variables as a function of a first weighted sum of the state variables, input variables, and internal delay variables with a set of time delays;
receiving a second description of the generalized state-space system based on the state-space system, the second description expressing channel variables as a function of a second weighted sum of the state variables, the input variables, and the internal delay variables;
receiving a third description of the generalized state-space system based on the state-space system, the third description expressing the outputs of the generalized state-space system as a function of a third weighted sum of the state variables, the input variables, and the internal delay variables;
simulating the generalized state-space system in a computing environment based on the first description, the second description and the third description; and
storing outputs of the simulated generalized state-space system.
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Abstract
A method and apparatus are provided to model, analyze, and build linear time invariant systems with delays. The method and apparatus model a linear time invariant system as a linear fractional transformation of matrices of a delay free linear time invariant model with a bank of pure delays. The method and apparatus of the present invention can further accommodate input delays and output delays associated with the linear time invariant system with delays.
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10 Claims
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1. A computer-readable storage medium that comprises computer-executable instructions that when executed perform the method of:
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receiving a first description of a generalized state-space system based on a state-space system, the first description expressing time derivatives of state variables as a function of a first weighted sum of the state variables, input variables, and internal delay variables with a set of time delays; receiving a second description of the generalized state-space system based on the state-space system, the second description expressing channel variables as a function of a second weighted sum of the state variables, the input variables, and the internal delay variables; receiving a third description of the generalized state-space system based on the state-space system, the third description expressing the outputs of the generalized state-space system as a function of a third weighted sum of the state variables, the input variables, and the internal delay variables; simulating the generalized state-space system in a computing environment based on the first description, the second description and the third description; and storing outputs of the simulated generalized state-space system. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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Specification