This paper addresses the sliding mode secure control problem for continuous-time cyber-physical systems (CPSs) subject to unmatched disturbances and actuator deception attacks. To capture different operating conditions and account for random component failures in CPSs, a Markov jumping model is introduced to characterize the system's component matrices. Next, a novel model-free integral sliding mode function and a corresponding sliding mode controller are presented to mitigate the impact of external disturbances and deception attacks on Markov jumping cyber-physical systems. An algorithm based on adaptive dynamic programming (ADP) and homotopic policy iteration (PI) is applied to develop the sliding mode controller, called the online homotopic ADP algorithm, which avoids the requirement for an initial stabilizing matrix compared to existing PI algorithms. Lastly, the mode-independent integral sliding mode control scheme is studied to a two-mode Markov jumping vertical take-off and landing helicopter system, providing guaranteed reachability of sliding variables and stability of sliding mode dynamics. Importantly, this is achieved without any reliance on knowledge of system dynamics.