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# SBSDS - Stability and Bifurcation of Switched Dynamical System

### Runner-up - DSWeb 2019 Tutorials on DS Software Contest, Junior Faculty Category

By Kuntal Mandal
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Stability and Bifurcation of Switched Dynamical System (SABSDS) is an automated software for the steady-state time -domain analysis as well as the stability analysis of Switched Dynamical Systems (SDS). It is based on the fundamental solution matrix and can be applied to any switching dynamical system.

This software achieves the following:

• To calculate the time domain behaviour of the system starting from any initial condition.
• To locate the periodic orbits (stable as well as unstable) and to compute their stability. This is done using the shooting method, where the computation of the monodromy matrix takes into account the switching events through appropriate saltation matrices. Thus, while the Newton-Raphson search converges on the periodic orbit, the Jacobian matrix also converges and hence the stability can be calculated with no extra computational effort. The program can do so even when each subsystem is nonlinear.
• To compute the bifurcation diagram, including the ability to follow periodic orbits.
• To perform small-signal analysis and to calculate the relevant transfer functions in s-domain. This is an extra offshoot of the computation of the monodromy matrix, incorporated into the program. This is vitally important for system designers.
• To have a graphical user interface (GUI) that allows the user to enter the system description, parameter values, and the switching conditions, with appropriate buttons to activate each computational function.

It is expected to be useful in carrying out a number of computations (fixed points, their stability, bifurcation diagram, phase space) in an efficient and simple way. This tool has no bar on problem size because each switching is considered separately by saltation matrices.

This software will help undergraduate student, post-graduate student and researchers to analyse complex switched dynamical system.

 Model ODEs Software Type Package Language MatLab Platform UnixLinuxWindowsMacOS Contact Person Kuntal Mandal