High-performance modeling and discrete-time sliding mode control of uncertain non-commensurate linear time invariant MIMO fractional order dynamic systems

Abstract

This paper primarily proposes an analytical solution to the set of coupled non-commensurate linear time invariant fractional order differential equations (representing Multi input Multi output (MIMO) fractional order dynamic systems). The proposed solution is reviewed and accurately truncated to have a short finite-memory and to demonstrate further compatibility for practical applications. It is also stated that this discrete-time approach is explicitly superior to any approach in continuous-time in terms of the possibility of implementation. Standards are provided for adequate truncation of the response with respect to the application. A novel discrete-time enhanced sliding mode control (ESMC) scheme is proposed for MIMO fractional order dynamic systems that can cope with parameter uncertainty while illustrating robustness against disturbance. Due to its structure, ESMC shows no sign of chattering in its control signal and employs no fractional operator in its structure; hence, computational cost of ESMC is minuscule. A novel mathematical method is also proposed for acquiring the stability bounds and solving linear matrix inequalities that arise in this problem. A famous MIMO fractional order dynamic system is presented and controlled under considerable disturbance and parameter uncertainty to render the merits of ESMC.