Controllability analysis for a class of linear quadratic conformable fractional game-based control systems

Controllability analysis for a class of linear quadratic conformable fractional game-based control systems (CFGBCSs) is investigated in this article. Supported by the definition and property of conformable fractional, the payoff function for linear quadratic CFGBCSs is proposed, and Nash equilibrium solution is obtained via variational method for Hamilton function correspondingly. Subsequently, the state transition matrix and controllability matrix are presented to deduce the sufficient and necessary conditions for the controllability of Nash equilibrium solution of time-varying linear quadratic CFGBCSs and time-invariant linear quadratic CFGBCSs, respectively. Finally, two numerical examples are furnished to justify the validity of the matrix full rank condition.