Department of Electrical and
Computer Engineering

*Linear Systems
Virtual Experiments*

This web site presents some virtual experiments related to
linear systems. This web site is intended to augment the course EEC 510 (Linear Systems) at

Linear vs. Nonlinear Systems - This experiment demonstrates the property of superposition for linear systems, and the lack of that property for nonlinear systems.

Linearization - This experiment demonstrates how nonlinear systems can be linearized around a nominal operating point. The behavior of the resultant linear system is quite similar to the nonlinear system. However, if the operating point of the linear system moves away from the nominal operating point, then the approximation quickly degrades.

System Realization - This experiment shows that there are an infinite number of realizations (i.e., state space descriptions) for any given transfer function. A minimal realization (i.e., a realization with the smallest number of states) is always both controllable and observable.

System Stability - This experiment demonstrates two types of stability: Lyapunov stability (also called internal stability), and BIBO (bounded input bounded output) stability (also called external stability).

State Feedback - This experiment demonstrates state feedback using the eigenvalue assignment method. We can assign the eignevalues of a controllable system at arbitrary points in the complex plane (subject to the complex conjugate constraint). Placing the eigenvalues farther to the left results in quicker regulation of the states, but it also results in larger control magnitudes.

**Acknowledgements**

The development of this web site was made possible by a grant from the University Center for Teaching and Learning. The applets were written in Visual J++ by Hrishikesh Godbole. The counter below was provided by digits.com.

Department of Electrical and Computer Engineering

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